id string | source string | formal_statement string | header string | lean4_code string | has_proof bool | proof_body string | natural_language null | lean_version string | split string | tags list | category null | metadata string | verification string | v4210_is_valid bool | v4210_compiles bool | v4210_has_sorry bool | v4210_latency_s float64 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
compfiles_Bulgaria1998P1 | compfiles | Copyright (c) 2023 David Renshaw. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Renshaw
-/
import Mathlib
/-!
# Bulgarian Mathematical Olympiad 1998, Problem 1
We will be considering colorings in 2 colors of n (distinct) points
A₁, A₂, ..., Aₙ. Call such a ... | /- | /-
Copyright (c) 2023 David Renshaw. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Renshaw
-/
import Mathlib
/-!
# Bulgarian Mathematical Olympiad 1998, Problem 1
We will be considering colorings in 2 colors of n (distinct) points
A₁, A₂, ..., Aₙ. Call such... | false | null | null | v4.29.0-rc6 | test | [
"competition"
] | null | {"filename": "Bulgaria1998P1.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": true, "errors": [], "timeout_s": 600.0, "latency_s": 34.5438, "verified_at": "2026-03-26T18:15:55.711664+00:00"}} | false | true | true | 34.5438 |
compfiles_Bulgaria1998P11 | compfiles | Copyright (c) 2023 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Renshaw, Adam Kurkiewicz
-/
import Mathlib
/-!
Bulgarian Mathematical Olympiad 1998, Problem 11
Let m,n be natural numbers such that
A = ((m + 3)ⁿ + 1) / (3m)
... | /- | /-
Copyright (c) 2023 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Renshaw, Adam Kurkiewicz
-/
import Mathlib
/-!
Bulgarian Mathematical Olympiad 1998, Problem 11
Let m,n be natural numbers such that
A = ((m + 3)ⁿ + 1) / (3m... | true | Copyright (c) 2023 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Renshaw, Adam Kurkiewicz
-/
import Mathlib
/-!
Bulgarian Mathematical Olympiad 1998, Problem 11
Let m,n be natural numbers such that
A = ((m + 3)ⁿ + 1) / (3m)
... | null | v4.29.0-rc6 | test | [
"competition"
] | null | {"filename": "Bulgaria1998P11.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["unknown tactic", "unsolved goals\ncase neg\nm n A : \u2115\nh : 3 * m * A = (m + 3) ^ 0 + 1\nn_gt_zero : \u00acn > 0\n\u22a2 Odd n \u2227 m \u2261 2 [MOD 3]", "unknown tactic", "unsolved goals\nm : \u2115\neven_m : Even m\nh : 0 < m\na : \u2115\nha : m = 2... | false | true | false | 40.3366 |
compfiles_Bulgaria1998P2 | compfiles | Copyright (c) 2023 David Renshaw. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Renshaw
-/
import Mathlib
/-!
# Bulgarian Mathematical Olympiad 1998, Problem 2
A convex quadrilateral ABCD has AD = CD and ∠DAB = ∠ABC < 90°.
The line through D and the midpoin... | /- | /-
Copyright (c) 2023 David Renshaw. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Renshaw
-/
import Mathlib
/-!
# Bulgarian Mathematical Olympiad 1998, Problem 2
A convex quadrilateral ABCD has AD = CD and ∠DAB = ∠ABC < 90°.
The line through D and the midp... | false | null | null | v4.29.0-rc6 | test | [
"competition"
] | null | {"filename": "Bulgaria1998P2.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": true, "errors": [], "timeout_s": 600.0, "latency_s": 33.2751, "verified_at": "2026-03-26T18:15:54.443933+00:00"}} | false | true | true | 33.2751 |
compfiles_Bulgaria1998P3 | compfiles | Copyright (c) 2023 David Renshaw. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Renshaw
-/
import Mathlib
/-!
# Bulgarian Mathematical Olympiad 1998, Problem 3
Let ℝ⁺ be the set of positive real numbers. Prove that there does not exist a function
f: ℝ⁺ → ℝ⁺... | /- | /-
Copyright (c) 2023 David Renshaw. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Renshaw
-/
import Mathlib
/-!
# Bulgarian Mathematical Olympiad 1998, Problem 3
Let ℝ⁺ be the set of positive real numbers. Prove that there does not exist a function
f: ℝ⁺ →... | true | Copyright (c) 2023 David Renshaw. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Renshaw
-/
import Mathlib
/-!
# Bulgarian Mathematical Olympiad 1998, Problem 3
Let ℝ⁺ be the set of positive real numbers. Prove that there does not exist a function
f: ℝ⁺ → ℝ⁺... | null | v4.29.0-rc6 | test | [
"competition"
] | null | {"filename": "Bulgaria1998P3.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["unknown identifier 'mul_lt_mul_iff_left\u2080'"], "timeout_s": 600.0, "latency_s": 35.1685, "verified_at": "2026-03-26T18:15:56.337288+00:00"}} | false | true | false | 35.1685 |
compfiles_Bulgaria1998P6 | compfiles | Copyright (c) 2023 David Renshaw. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Renshaw
-/
import Mathlib
/-!
# Bulgarian Mathematical Olympiad 1998, Problem 6
Prove that the equation
x²y² = z²(z² - x² - y²)
has no solutions in positive integers.
-/... | /- | /-
Copyright (c) 2023 David Renshaw. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Renshaw
-/
import Mathlib
/-!
# Bulgarian Mathematical Olympiad 1998, Problem 6
Prove that the equation
x²y² = z²(z² - x² - y²)
has no solutions in positive integers.
... | false | null | null | v4.29.0-rc6 | test | [
"competition"
] | null | {"filename": "Bulgaria1998P6.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": true, "errors": [], "timeout_s": 600.0, "latency_s": 1.6128, "verified_at": "2026-03-26T18:15:56.056907+00:00"}} | false | true | true | 1.6128 |
compfiles_Bulgaria1998P8 | compfiles | Copyright (c) 2023 David Renshaw. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Renshaw
-/
import Mathlib
/-!
# Bulgarian Mathematical Olympiad 1998, Problem 8
The polynomials Pₙ(x,y) for n = 1, 2, ... are defined by P₁(x,y) = 1 and
Pₙ₊₁(x,y) = (x + y - 1)... | /- | /-
Copyright (c) 2023 David Renshaw. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Renshaw
-/
import Mathlib
/-!
# Bulgarian Mathematical Olympiad 1998, Problem 8
The polynomials Pₙ(x,y) for n = 1, 2, ... are defined by P₁(x,y) = 1 and
Pₙ₊₁(x,y) = (x + y -... | true | Copyright (c) 2023 David Renshaw. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Renshaw
-/
import Mathlib
/-!
# Bulgarian Mathematical Olympiad 1998, Problem 8
The polynomials Pₙ(x,y) for n = 1, 2, ... are defined by P₁(x,y) = 1 and
Pₙ₊₁(x,y) = (x + y - 1)... | null | v4.29.0-rc6 | test | [
"competition"
] | null | {"filename": "Bulgaria1998P8.lean"} | {"v4.21.0": {"is_valid": true, "has_sorry": false, "errors": [], "timeout_s": 600.0, "latency_s": 1.7539, "verified_at": "2026-03-26T18:15:57.465676+00:00"}} | true | true | false | 1.7539 |
compfiles_CIIM2022P6 | compfiles | Copyright (c) 2024 David Renshaw. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Renshaw
-/
import Mathlib
/-!
# Iberoamerican Interuniversity Mathematics Competition 2022, Problem 6
Given a positive integer m, let d(m) be the number of postive
divisors of m... | /- | /-
Copyright (c) 2024 David Renshaw. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Renshaw
-/
import Mathlib
/-!
# Iberoamerican Interuniversity Mathematics Competition 2022, Problem 6
Given a positive integer m, let d(m) be the number of postive
divisors o... | false | null | null | v4.29.0-rc6 | test | [
"competition"
] | null | {"filename": "CIIM2022P6.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": true, "errors": [], "timeout_s": 600.0, "latency_s": 0.0288, "verified_at": "2026-03-26T18:15:56.085817+00:00"}} | false | true | true | 0.0288 |
compfiles_Canada1998P3 | compfiles | Copyright (c) 2023 David Renshaw. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Renshaw
-/
import Mathlib
/-!
Canadian Mathematical Olympiad 1998, Problem 3
Let n be a natural number such that n ≥ 2. Show that
(1/(n + 1))(1 + 1/3 + ... + 1/(2n - 1)) > (1... | /- | /-
Copyright (c) 2023 David Renshaw. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Renshaw
-/
import Mathlib
/-!
Canadian Mathematical Olympiad 1998, Problem 3
Let n be a natural number such that n ≥ 2. Show that
(1/(n + 1))(1 + 1/3 + ... + 1/(2n - 1)) >... | true | Copyright (c) 2023 David Renshaw. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Renshaw
-/
import Mathlib
/-!
Canadian Mathematical Olympiad 1998, Problem 3
Let n be a natural number such that n ≥ 2. Show that
(1/(n + 1))(1 + 1/3 + ... + 1/(2n - 1)) > (1... | null | v4.29.0-rc6 | test | [
"competition"
] | null | {"filename": "Canada1998P3.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["unknown tactic", "unknown constant 'Finset.nonempty_range_add_one'", "unsolved goals\nm : \u2115\nih :\n (\u2191m.succ.succ + 1) * \u2211 i \u2208 Finset.range m.succ.succ, 1 / (2 * \u2191i + 2) <\n \u2191m.succ.succ * \u2211 i \u2208 Finset.range m.su... | false | true | false | 5.2525 |
compfiles_Canada1998P5 | compfiles | Copyright (c) 2023 David Renshaw. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Renshaw
-/
import Mathlib
/-!
Canadian Mathematical Olympiad 1998, Problem 5
Let m be a positive integer. Define the sequence {aₙ} by a₀ = 0,
a₁ = m, and aₙ₊₁ = m²aₙ - aₙ₋₁ for ... | /- | /-
Copyright (c) 2023 David Renshaw. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Renshaw
-/
import Mathlib
/-!
Canadian Mathematical Olympiad 1998, Problem 5
Let m be a positive integer. Define the sequence {aₙ} by a₀ = 0,
a₁ = m, and aₙ₊₁ = m²aₙ - aₙ₋₁ f... | false | null | null | v4.29.0-rc6 | test | [
"competition"
] | null | {"filename": "Canada1998P5.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": true, "errors": [], "timeout_s": 600.0, "latency_s": 0.0672, "verified_at": "2026-03-26T18:15:56.404638+00:00"}} | false | true | true | 0.0672 |
compfiles_Egmo2023P1 | compfiles | Copyright (c) 2025 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ansar Azharov
-/
import Mathlib
/-!
# European Girls' Mathematical Olympiad 2023, Problem 1
There are n ≥ 3 positive real numbers a_1, a_2, . . . , a_n. For each 1 ≤ i ≤ ... | /- | /-
Copyright (c) 2025 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ansar Azharov
-/
import Mathlib
/-!
# European Girls' Mathematical Olympiad 2023, Problem 1
There are n ≥ 3 positive real numbers a_1, a_2, . . . , a_n. For each 1 ≤ i... | true | Copyright (c) 2025 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ansar Azharov
-/
import Mathlib
/-!
# European Girls' Mathematical Olympiad 2023, Problem 1
There are n ≥ 3 positive real numbers a_1, a_2, . . . , a_n. For each 1 ≤ i ≤ ... | null | v4.29.0-rc6 | test | [
"competition"
] | null | {"filename": "Egmo2023P1.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["failed to prove positivity/nonnegativity/nonzeroness", "unsolved goals\ncase intro.intro\nn : \u2115\ninst\u271d : NeZero n\nx\u271d : n \u2265 3\na : Fin n \u2192 \u211d\nha : \u2200 (i : Fin n), a i > 0\nb : Fin n \u2192 \u211d\nhb : \u2200 (i : Fin n), ... | false | true | false | 0.2509 |
compfiles_Hungary1998P6 | compfiles | Copyright (c) 2023 David Renshaw. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Renshaw
-/
import Mathlib
/-!
# Hungarian Mathematical Olympiad 1998, Problem 6
Let x, y, z be integers with z > 1. Show that
(x + 1)² + (x + 2)² + ... + (x + 99)² ≠ yᶻ.
-/
n... | /- | /-
Copyright (c) 2023 David Renshaw. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Renshaw
-/
import Mathlib
/-!
# Hungarian Mathematical Olympiad 1998, Problem 6
Let x, y, z be integers with z > 1. Show that
(x + 1)² + (x + 2)² + ... + (x + 99)² ≠ yᶻ.
-/... | true | Copyright (c) 2023 David Renshaw. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Renshaw
-/
import Mathlib
/-!
# Hungarian Mathematical Olympiad 1998, Problem 6
Let x, y, z be integers with z > 1. Show that
(x + 1)² + (x + 2)² + ... + (x + 99)² ≠ yᶻ.
-/
n... | null | v4.29.0-rc6 | test | [
"competition"
] | null | {"filename": "Hungary1998P6.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["unknown tactic", "unsolved goals\ncase intro.succ.succ\nx y : \u2124\nh2 : \u2211 i \u2208 Finset.range 99, x ^ 2 = 99 * x ^ 2\nh4 : \u2211 i \u2208 Finset.range 99, (\u2191i + 1) = \u2211 i \u2208 Finset.range 100, \u2191i\nh5 : \u2211 i \u2208 Finset.ran... | false | true | false | 1.7075 |
compfiles_Imo1959P1 | compfiles | Copyright (c) 2020 Kevin Lacker. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Lacker
-/
import Mathlib
/-!
# International Mathematical Olympiad 1959, Problem 1.
Prove that the fraction `(21n+4)/(14n+3)` is irreducible for every
natural number `n`.
-/
name... | /- | /-
Copyright (c) 2020 Kevin Lacker. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Lacker
-/
import Mathlib
/-!
# International Mathematical Olympiad 1959, Problem 1.
Prove that the fraction `(21n+4)/(14n+3)` is irreducible for every
natural number `n`.
-/
n... | true | Copyright (c) 2020 Kevin Lacker. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Lacker
-/
import Mathlib
/-!
# International Mathematical Olympiad 1959, Problem 1.
Prove that the fraction `(21n+4)/(14n+3)` is irreducible for every
natural number `n`.
-/
name... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo1959P1.lean"} | {"v4.21.0": {"is_valid": true, "has_sorry": false, "errors": [], "timeout_s": 600.0, "latency_s": 0.0842, "verified_at": "2026-03-26T18:15:57.549955+00:00"}} | true | true | false | 0.0842 |
compfiles_Imo1959P2 | compfiles | Copyright (c) 2024 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Mathlib
/-!
# International Mathematical Olympiad 1959, Problem 2
For what real values of x is
√(x+√(2x-1)) + √(x-√(2x-1)) = A,
given:
(a) A = √2
(b)... | /- | /-
Copyright (c) 2024 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Mathlib
/-!
# International Mathematical Olympiad 1959, Problem 2
For what real values of x is
√(x+√(2x-1)) + √(x-√(2x-1)) = A,
given:
(a) A = √2
... | true | Copyright (c) 2024 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Mathlib
/-!
# International Mathematical Olympiad 1959, Problem 2
For what real values of x is
√(x+√(2x-1)) + √(x-√(2x-1)) = A,
given:
(a) A = √2
(b)... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo1959P2.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["unknown identifier 'sqrt'", "unknown identifier 'sqrt'", "unknown identifier 'sqrt'", "unknown identifier 'sqrt'", "function expected at\n sqrt\nterm has type\n ?m.449", "function expected at\n sqrt\nterm has type\n ?m.449", "function expected at\n sq... | false | true | false | 0.8435 |
compfiles_Imo1960P1 | compfiles | Copyright (c) 2020 Kevin Lacker. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Lacker
-/
import Mathlib
/-!
# International Mathematical Olympiad 1960, Problem 1
Determine all three-digit numbers N having the property that N is divisible by 11, and
N/11 is e... | /- | /-
Copyright (c) 2020 Kevin Lacker. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Lacker
-/
import Mathlib
/-!
# International Mathematical Olympiad 1960, Problem 1
Determine all three-digit numbers N having the property that N is divisible by 11, and
N/11 i... | true | Copyright (c) 2020 Kevin Lacker. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Lacker
-/
import Mathlib
/-!
# International Mathematical Olympiad 1960, Problem 1
Determine all three-digit numbers N having the property that N is divisible by 11, and
N/11 is e... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo1960P1.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["unknown identifier 'digits_ne_nil_iff_ne_zero.mp'", "unknown identifier 'lt_base_pow_length_digits''", "unknown tactic", "unsolved goals\ncase neg\nc : \u2115\nH' : c = sumOfSquares (Nat.digits 10 (c * 11)) \u2192 c = 50 \u2228 c = 73\nH : \u2200 m < c * 1... | false | true | false | 4.1061 |
compfiles_Imo1960P2 | compfiles | Copyright (c) 2024 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Mathlib
/-!
# International Mathematical Olympiad 1960, Problem 2
For what values of the variable $x$ does the following inequality hold:
\[\dfrac{4x^2}{(1... | /- | /-
Copyright (c) 2024 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Mathlib
/-!
# International Mathematical Olympiad 1960, Problem 2
For what values of the variable $x$ does the following inequality hold:
\[\dfrac{4x^2}... | true | Copyright (c) 2024 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Mathlib
/-!
# International Mathematical Olympiad 1960, Problem 2
For what values of the variable $x$ does the following inequality hold:
\[\dfrac{4x^2}{(1... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo1960P2.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["function expected at\n sqrt\nterm has type\n ?m.67", "function expected at\n sqrt\nterm has type\n ?m.2102", "unknown identifier 'Ico'", "unsolved goals\ncase inl\n\u22a2 (\u2203 x, Nonempty x) \u2227 1 - sorry () = 0", "unsolved goals\ncase inr.inl\nx... | false | true | false | 1.6333 |
compfiles_Imo1961P1 | compfiles | Copyright (c) 2020 David Renshaw. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Renshaw, Roozbeh Yousefzadeh
-/
import Mathlib
/-!
# International Mathematical Olympiad 1961, Problem 1.
Given constants a and b, solve the system of equations
x ... | /- | /-
Copyright (c) 2020 David Renshaw. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Renshaw, Roozbeh Yousefzadeh
-/
import Mathlib
/-!
# International Mathematical Olympiad 1961, Problem 1.
Given constants a and b, solve the system of equations
... | true | Copyright (c) 2020 David Renshaw. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Renshaw, Roozbeh Yousefzadeh
-/
import Mathlib
/-!
# International Mathematical Olympiad 1961, Problem 1.
Given constants a and b, solve the system of equations
x ... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo1961P1.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["`grind` failed\ncase grind\nx y z a b : \u211d\nleft : 0 < x\nleft_1 : 0 < y\nright_1 : 0 < z\nh\u2081 : [x, y, z].Nodup\nh\u2082 : x + y + z = a\nh\u2083 : x ^ 2 + y ^ 2 + z ^ 2 = b ^ 2\nh\u2084 : x * y = z ^ 2\nha : 0 < a\nh\u2087 : (x + y + z) * (x + y ... | false | true | false | 7.9973 |
compfiles_Imo1961P2 | compfiles | Copyright (c) 2025 lean-tom. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: lean-tom (with assistance from Gemini)
-/
import Mathlib
/-!
# International Mathematical Olympiad 1961, Problem 2
Let $a, b, c$ be the sides of a triangle, and $T$ its area. Prove:
$$ a^2... | /- | /-
Copyright (c) 2025 lean-tom. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: lean-tom (with assistance from Gemini)
-/
import Mathlib
/-!
# International Mathematical Olympiad 1961, Problem 2
Let $a, b, c$ be the sides of a triangle, and $T$ its area. Prove:
$$ ... | true | Copyright (c) 2025 lean-tom. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: lean-tom (with assistance from Gemini)
-/
import Mathlib
/-!
# International Mathematical Olympiad 1961, Problem 2
Let $a, b, c$ be the sides of a triangle, and $T$ its area. Prove:
$$ a^2... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo1961P2.lean"} | {"v4.21.0": {"is_valid": true, "has_sorry": false, "errors": [], "timeout_s": 600.0, "latency_s": 1.967, "verified_at": "2026-03-26T18:16:09.994999+00:00"}} | true | true | false | 1.967 |
compfiles_Imo1961P3 | compfiles | Copyright (c) 2024 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Mathlib
/-!
# International Mathematical Olympiad 1961, Problem 3
Solve the equation
cosⁿ x - sinⁿ x = 1,
where n is a given positive intege... | /- | /-
Copyright (c) 2024 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Mathlib
/-!
# International Mathematical Olympiad 1961, Problem 3
Solve the equation
cosⁿ x - sinⁿ x = 1,
where n is a given positive int... | true | Copyright (c) 2024 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Mathlib
/-!
# International Mathematical Olympiad 1961, Problem 3
Solve the equation
cosⁿ x - sinⁿ x = 1,
where n is a given positive intege... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo1961P3.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["unknown identifier 'eq_zero_of_pow_eq_zero'"], "timeout_s": 600.0, "latency_s": 1.3206, "verified_at": "2026-03-26T18:16:09.348807+00:00"}} | false | true | false | 1.3206 |
compfiles_Imo1962P1 | compfiles | Copyright (c) 2020 Kevin Lacker. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Lacker
-/
import Mathlib
/-!
# International Mathematical Olympiad 1962, Problem 1
Find the smallest natural number $n$ which has the following properties:
(a) Its decimal repres... | /- | /-
Copyright (c) 2020 Kevin Lacker. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Lacker
-/
import Mathlib
/-!
# International Mathematical Olympiad 1962, Problem 1
Find the smallest natural number $n$ which has the following properties:
(a) Its decimal rep... | true | Copyright (c) 2020 Kevin Lacker. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Lacker
-/
import Mathlib
/-!
# International Mathematical Olympiad 1962, Problem 1
Find the smallest natural number $n$ which has the following properties:
(a) Its decimal repres... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo1962P1.lean"} | {"v4.21.0": {"is_valid": true, "has_sorry": false, "errors": [], "timeout_s": 120, "latency_s": 2.0913, "verified_at": "2026-03-30T14:38:26.360701+00:00"}} | true | true | false | 2.0913 |
compfiles_Imo1962P2 | compfiles | Copyright (c) 2024 David Renshaw. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Renshaw
-/
import Mathlib
/-!
# International Mathematical Olympiad 1962, Problem 2
Determine all real numbers x which satisfy
√(3 - x) - √(x + 1) > 1/2.
-/
namespace Imo196... | /- | /-
Copyright (c) 2024 David Renshaw. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Renshaw
-/
import Mathlib
/-!
# International Mathematical Olympiad 1962, Problem 2
Determine all real numbers x which satisfy
√(3 - x) - √(x + 1) > 1/2.
-/
namespace Imo... | true | Copyright (c) 2024 David Renshaw. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Renshaw
-/
import Mathlib
/-!
# International Mathematical Olympiad 1962, Problem 2
Determine all real numbers x which satisfy
√(3 - x) - √(x + 1) > 1/2.
-/
namespace Imo196... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo1962P2.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["`grind` failed\ncase grind\nx : \u211d\nh : \u00ac(15 / 8) ^ 2 - (3 - x) * (x + 1) = (x - (1 + \u221a31 / 8)) * (x - (1 - \u221a31 / 8))\n\u22a2 False\n[grind] Goal diagnostics\n [facts] Asserted facts\n [prop] \u00ac(15 / 8) ^ 2 - (3 - x) * (x + 1) = ... | false | true | false | 2.5601 |
compfiles_Imo1962P4 | compfiles | Copyright (c) 2020 Kevin Lacker. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Lacker, Heather Macbeth
-/
import Mathlib
/-!
# International Mathematics Olympiad 1962, Problem 4
Solve the equation
cos² x + cos² (2 * x) + cos² (3 * x) = 1.
-/
open Real
... | /- | /-
Copyright (c) 2020 Kevin Lacker. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Lacker, Heather Macbeth
-/
import Mathlib
/-!
# International Mathematics Olympiad 1962, Problem 4
Solve the equation
cos² x + cos² (2 * x) + cos² (3 * x) = 1.
-/
open Re... | true | Copyright (c) 2020 Kevin Lacker. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Lacker, Heather Macbeth
-/
import Mathlib
/-!
# International Mathematics Olympiad 1962, Problem 4
Solve the equation
cos² x + cos² (2 * x) + cos² (3 * x) = 1.
-/
open Real
... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo1962P4.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["unknown identifier 'cos'", "unknown identifier 'cos'", "unknown identifier 'cos'", "unknown identifier '\u03c0'", "unknown identifier '\u03c0'", "unknown identifier 'cos'", "unknown identifier 'cos'", "unknown identifier 'cos'", "function expected at\n co... | false | true | false | 0.7208 |
compfiles_Imo1963P1 | compfiles | Copyright (c) 2024 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Hongyu Ouyang
-/
import Mathlib
/-!
# International Mathematical Olympiad 1963, Problem 1
Find all real roots of the equation
√(x²-p) + 2√(x²-1) = x
where *p* is a re... | /- | /-
Copyright (c) 2024 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Hongyu Ouyang
-/
import Mathlib
/-!
# International Mathematical Olympiad 1963, Problem 1
Find all real roots of the equation
√(x²-p) + 2√(x²-1) = x
where *p* is a... | true | Copyright (c) 2024 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Hongyu Ouyang
-/
import Mathlib
/-!
# International Mathematical Olympiad 1963, Problem 1
Find all real roots of the equation
√(x²-p) + 2√(x²-1) = x
where *p* is a re... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo1963P1.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["unknown identifier 'mul_le_mul_iff_left\u2080'", "unsolved goals\np x : \u211d\nh1 : x ^ 2 - p \u2265 0\nh2 : x ^ 2 - 1 \u2265 0\nxge0 : x \u2265 0\nxp : p + 4 - 4 * x ^ 2 \u2265 0\nhp : p < 2\ntmp : 4 - 2 * p > 0\n\u22a2 x ^ 2 * 4 * (4 - 2 * p) = (p - 4) ... | false | true | false | 3.498 |
compfiles_Imo1963P4 | compfiles | Copyright (c) 2024 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Maximiliano Onofre-Martínez
-/
import Mathlib
/-!
# International Mathematical Olympiad 1963, Problem 4
Find all solutions x₁,x₂,x₃,x₄,x₅ of the system
x₅ + x₂ = yx₁
... | /- | /-
Copyright (c) 2024 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Maximiliano Onofre-Martínez
-/
import Mathlib
/-!
# International Mathematical Olympiad 1963, Problem 4
Find all solutions x₁,x₂,x₃,x₄,x₅ of the system
x₅ + x₂ = yx... | true | Copyright (c) 2024 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Maximiliano Onofre-Martínez
-/
import Mathlib
/-!
# International Mathematical Olympiad 1963, Problem 4
Find all solutions x₁,x₂,x₃,x₄,x₅ of the system
x₅ + x₂ = yx₁
... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo1963P4.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["`grind` failed\ncase grind.1.1\nx\u2081 x\u2082 x\u2083 x\u2084 x\u2085 y : \u211d\nh :\n ((x\u2081, x\u2082, x\u2083, x\u2084, x\u2085) \u2208\n {x |\n x.1 = 0 \u2227 x.2.1 = 0 \u2227 x.2.2.1 = 0 \u2227 x.2.2.2.1 = 0 \u2227 x.2.2.2.2 = 0 \u22... | false | true | false | 0.2304 |
compfiles_Imo1963P5 | compfiles | Copyright (c) 2024 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Hongyu Ouyang
-/
import Mathlib
/-!
# International Mathematical Olympiad 1963, Problem 5
Prove that cos(π/7) - cos(2π/7) + cos(3π/7) = 1/2.
-/
namespace Imo1963P5
open... | /- | /-
Copyright (c) 2024 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Hongyu Ouyang
-/
import Mathlib
/-!
# International Mathematical Olympiad 1963, Problem 5
Prove that cos(π/7) - cos(2π/7) + cos(3π/7) = 1/2.
-/
namespace Imo1963P5
o... | true | Copyright (c) 2024 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Hongyu Ouyang
-/
import Mathlib
/-!
# International Mathematical Olympiad 1963, Problem 5
Prove that cos(π/7) - cos(2π/7) + cos(3π/7) = 1/2.
-/
namespace Imo1963P5
open... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo1963P5.lean"} | {"v4.21.0": {"is_valid": true, "has_sorry": false, "errors": [], "timeout_s": 600.0, "latency_s": 1.3886, "verified_at": "2026-03-26T18:16:10.968197+00:00"}} | true | true | false | 1.3886 |
compfiles_Imo1964P1 | compfiles | Copyright (c) 2023 David Renshaw. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Renshaw, Anand Rao, Harald Carlens
-/
import Mathlib
/-!
# International Mathematical Olympiad 1964, Problem 1
(a) Find all natural numbers n for which 2ⁿ - 1 is divisible by 7.... | /- | /-
Copyright (c) 2023 David Renshaw. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Renshaw, Anand Rao, Harald Carlens
-/
import Mathlib
/-!
# International Mathematical Olympiad 1964, Problem 1
(a) Find all natural numbers n for which 2ⁿ - 1 is divisible by... | true | Copyright (c) 2023 David Renshaw. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Renshaw, Anand Rao, Harald Carlens
-/
import Mathlib
/-!
# International Mathematical Olympiad 1964, Problem 1
(a) Find all natural numbers n for which 2ⁿ - 1 is divisible by 7.... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo1964P1.lean"} | {"v4.21.0": {"is_valid": true, "has_sorry": false, "errors": [], "timeout_s": 600.0, "latency_s": 0.3715, "verified_at": "2026-03-26T18:16:10.366632+00:00"}} | true | true | false | 0.3715 |
compfiles_Imo1964P2 | compfiles | Copyright (c) 2024 David Renshaw. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Renshaw
-/
import Mathlib
/-!
# International Mathematical Olympiad 1964, Problem 2
Suppose that a,b,c are the side lengths of a triangle. Prove that
a²(b + c - a) + b²(c + ... | /- | /-
Copyright (c) 2024 David Renshaw. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Renshaw
-/
import Mathlib
/-!
# International Mathematical Olympiad 1964, Problem 2
Suppose that a,b,c are the side lengths of a triangle. Prove that
a²(b + c - a) + b²(c... | true | Copyright (c) 2024 David Renshaw. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Renshaw
-/
import Mathlib
/-!
# International Mathematical Olympiad 1964, Problem 2
Suppose that a,b,c are the side lengths of a triangle. Prove that
a²(b + c - a) + b²(c + ... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo1964P2.lean"} | {"v4.21.0": {"is_valid": true, "has_sorry": false, "errors": [], "timeout_s": 600.0, "latency_s": 1.1175, "verified_at": "2026-03-26T18:16:11.484202+00:00"}} | true | true | false | 1.1175 |
compfiles_Imo1964P4 | compfiles | Copyright (c) 2023 David Renshaw. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Renshaw
-/
import Aesop
import Mathlib
/-!
# International Mathematical Olympiad 1964, Problem 4
Seventeen people correspond by mail with one another -- each one with
all the re... | /- | /-
Copyright (c) 2023 David Renshaw. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Renshaw
-/
import Aesop
import Mathlib
/-!
# International Mathematical Olympiad 1964, Problem 4
Seventeen people correspond by mail with one another -- each one with
all the... | true | Copyright (c) 2023 David Renshaw. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Renshaw
-/
import Aesop
import Mathlib
/-!
# International Mathematical Olympiad 1964, Problem 4
Seventeen people correspond by mail with one another -- each one with
all the re... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo1964P4.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["unknown tactic", "unsolved goals\nPerson Topic : Type\ninst\u271d\u00b3 : Fintype Person\ninst\u271d\u00b2 : DecidableEq Person\ninst\u271d\u00b9 : Fintype Topic\ninst\u271d : DecidableEq Topic\ncard_person : 5 < Fintype.card Person\ncard_topic : Fintype.c... | false | true | false | 0.068 |
compfiles_Imo1965P1 | compfiles | Copyright (c) 2024 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad
-/
import Mathlib
/-!
# International Mathematical Olympiad 1965, Problem 1
Determine all values x in the interval 0 ≤ x ≤ 2π which
satisfy the inequality
... | /- | /-
Copyright (c) 2024 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad
-/
import Mathlib
/-!
# International Mathematical Olympiad 1965, Problem 1
Determine all values x in the interval 0 ≤ x ≤ 2π which
satisfy the inequalit... | true | Copyright (c) 2024 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad
-/
import Mathlib
/-!
# International Mathematical Olympiad 1965, Problem 1
Determine all values x in the interval 0 ≤ x ≤ 2π which
satisfy the inequality
... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo1965P1.lean"} | {"v4.21.0": {"is_valid": true, "has_sorry": false, "errors": [], "timeout_s": 600.0, "latency_s": 5.5324, "verified_at": "2026-03-26T18:16:16.189337+00:00"}} | true | true | false | 5.5324 |
compfiles_Imo1965P2 | compfiles | Copyright (c) 2024 David Renshaw. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Renshaw
-/
import Mathlib
/-!
# International Mathematical Olympiad 1965, Problem 2
Suppose that
a₁₁x₁ + a₁₂x₂ + a₁₃x₃ = 0
a₂₁x₁ + a₂₂x₂ + a₂₃x₃ = 0
a₃₁x₁ + a₃₂x₂ + a₃₃x₃ ... | /- | /-
Copyright (c) 2024 David Renshaw. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Renshaw
-/
import Mathlib
/-!
# International Mathematical Olympiad 1965, Problem 2
Suppose that
a₁₁x₁ + a₁₂x₂ + a₁₃x₃ = 0
a₂₁x₁ + a₂₂x₂ + a₂₃x₃ = 0
a₃₁x₁ + a₃₂x₂ + a₃₃... | true | Copyright (c) 2024 David Renshaw. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Renshaw
-/
import Mathlib
/-!
# International Mathematical Olympiad 1965, Problem 2
Suppose that
a₁₁x₁ + a₁₂x₂ + a₁₃x₃ = 0
a₂₁x₁ + a₂₂x₂ + a₂₃x₃ = 0
a₃₁x₁ + a₃₂x₂ + a₃₃x₃ ... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo1965P2.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["unknown identifier 'mul_le_mul_iff_left\u2080'"], "timeout_s": 600.0, "latency_s": 2.4826, "verified_at": "2026-03-26T18:16:13.450914+00:00"}} | false | true | false | 2.4826 |
compfiles_Imo1965P4 | compfiles | Copyright (c) 2025 The Compfiles Authors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Rydh
-/
import Mathlib
/-!
# International Mathematical Olympiad 1965, Problem 4
Find all sets of four real numbers x₁, x₂, x₃, x₄ such that the sum of any one
and the ... | /- | /-
Copyright (c) 2025 The Compfiles Authors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Rydh
-/
import Mathlib
/-!
# International Mathematical Olympiad 1965, Problem 4
Find all sets of four real numbers x₁, x₂, x₃, x₄ such that the sum of any one
and t... | true | Copyright (c) 2025 The Compfiles Authors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Rydh
-/
import Mathlib
/-!
# International Mathematical Olympiad 1965, Problem 4
Find all sets of four real numbers x₁, x₂, x₃, x₄ such that the sum of any one
and the ... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo1965P4.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["unexpected identifier; expected ']'", "unexpected identifier; expected ']'", "`grind` failed\ncase grind\nS : Multiset \u211d\nhcard : S.card = 4\nhprod : \u2200 x \u2208 S, x + (S.erase x).prod = 2\nhS_nonempty : \u00acS = \u2205\nx : \u211d\nhx : x \u220... | false | true | false | 1.5157 |
compfiles_Imo1966P1 | compfiles | Copyright (c) 2025 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Shalev Wengrowsky
-/
import Mathlib
/-!
# International Mathematical Olympiad 1966, Problem 1.
In a mathematical contest, three problems, A, B, C were posed. Among the
par... | /- | /-
Copyright (c) 2025 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Shalev Wengrowsky
-/
import Mathlib
/-!
# International Mathematical Olympiad 1966, Problem 1.
In a mathematical contest, three problems, A, B, C were posed. Among the
... | true | Copyright (c) 2025 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Shalev Wengrowsky
-/
import Mathlib
/-!
# International Mathematical Olympiad 1966, Problem 1.
In a mathematical contest, three problems, A, B, C were posed. Among the
par... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo1966P1.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["unknown tactic", "unsolved goals\nU : Type u_1\ninst\u271d : DecidableEq U\na b c d e : \u2115\nx\u271d : a + b + c + d + e = 25\nh2 : b + d = 2 * (c + d)\nh3 : a = 1 + 25 - a - b - c - d\nh4 : a = b + c\n\u22a2 b = 6", "unsolved goals\nU : Type u_1\ninst\... | false | true | false | 5.6142 |
compfiles_Imo1966P4 | compfiles | Copyright (c) 2024 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Pedro Duailibe
-/
import Mathlib
/-!
# International Mathematical Olympiad 1966, Problem 4
Prove that for every natural number n and for every real
number x that is not o... | /- | /-
Copyright (c) 2024 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Pedro Duailibe
-/
import Mathlib
/-!
# International Mathematical Olympiad 1966, Problem 4
Prove that for every natural number n and for every real
number x that is no... | true | Copyright (c) 2024 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Pedro Duailibe
-/
import Mathlib
/-!
# International Mathematical Olympiad 1966, Problem 4
Prove that for every natural number n and for every real
number x that is not o... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo1966P4.lean"} | {"v4.21.0": {"is_valid": true, "has_sorry": false, "errors": [], "timeout_s": 600.0, "latency_s": 0.6322, "verified_at": "2026-03-26T18:16:13.632420+00:00"}} | true | true | false | 0.6322 |
compfiles_Imo1966P5 | compfiles | Copyright (c) 2025 Roozbeh Yousefzadeh. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Roozbeh Yousefzadeh, Benpigchu
-/
import Mathlib
/-!
# International Mathematical Olympiad 1966, Problem 5
Solve the system of equations
|a_1 - a_2| x_2 +|a_1 - a_3| x_3 +|a_... | /- | /-
Copyright (c) 2025 Roozbeh Yousefzadeh. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Roozbeh Yousefzadeh, Benpigchu
-/
import Mathlib
/-!
# International Mathematical Olympiad 1966, Problem 5
Solve the system of equations
|a_1 - a_2| x_2 +|a_1 - a_3| x_3 +... | true | Copyright (c) 2025 Roozbeh Yousefzadeh. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Roozbeh Yousefzadeh, Benpigchu
-/
import Mathlib
/-!
# International Mathematical Olympiad 1966, Problem 5
Solve the system of equations
|a_1 - a_2| x_2 +|a_1 - a_3| x_3 +|a_... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo1966P5.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["unknown tactic", "unsolved goals\nn : \u2115\nhn : 2 \u2264 n\na : Fin n \u2192 \u211d\nha : Function.Injective a\ni : Fin n\n\u22a2 0 < n", "unknown tactic", "tactic 'rewrite' failed, did not find instance of the pattern in the target expression\n nth_sm... | false | true | false | 1.2552 |
compfiles_Imo1967P3 | compfiles | Copyright (c) 2025 Roozbeh Yousefzadeh. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Roozbeh Yousefzadeh
-/
import Mathlib
/-!
# International Mathematical Olympiad 1967, Problem 3
Let $k, m, n$ be natural numbers such that m + k + 1 is a prime greater
than n + ... | /- | /-
Copyright (c) 2025 Roozbeh Yousefzadeh. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Roozbeh Yousefzadeh
-/
import Mathlib
/-!
# International Mathematical Olympiad 1967, Problem 3
Let $k, m, n$ be natural numbers such that m + k + 1 is a prime greater
than n... | true | Copyright (c) 2025 Roozbeh Yousefzadeh. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Roozbeh Yousefzadeh
-/
import Mathlib
/-!
# International Mathematical Olympiad 1967, Problem 3
Let $k, m, n$ be natural numbers such that m + k + 1 is a prime greater
than n + ... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo1967P3.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["`grind` failed\ncase grind.1.1.2\nc : \u2115 \u2192 \u2115\nh\u2081 : \u2200 (s : \u2115), c s = s * (s + 1)\na b : \u2115\nh : \u00aca + a ^ 2 - (b + b ^ 2) = a * (a + b + 1) - b * (a + b + 1)\nh_1 : -1 * \u2191a + \u2191b + -1 * \u2191(a ^ 2) + \u2191(b ... | false | true | false | 1.4826 |
compfiles_Imo1967P5 | compfiles | Copyright (c) 2025 The Compfiles Authors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Rydh
-/
import Mathlib
/-!
# International Mathematical Olympiad 1967, Problem 5
Consider the sequence {cₙ}, where
c₁ = a₁ + a₂ + ... + a₈
c₂ = a₁² + a₂² + ..... | /- | /-
Copyright (c) 2025 The Compfiles Authors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Rydh
-/
import Mathlib
/-!
# International Mathematical Olympiad 1967, Problem 5
Consider the sequence {cₙ}, where
c₁ = a₁ + a₂ + ... + a₈
c₂ = a₁² + a₂² +... | true | Copyright (c) 2025 The Compfiles Authors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Rydh
-/
import Mathlib
/-!
# International Mathematical Olympiad 1967, Problem 5
Consider the sequence {cₙ}, where
c₁ = a₁ + a₂ + ... + a₈
c₂ = a₁² + a₂² + ..... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo1967P5.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["unknown tactic", "unsolved goals\nI : Finset (Fin 8)\na : Fin 8 \u2192 \u211d\nh\u2081 : {n | \u2211 i \u2208 I, a i ^ n = 0}.Infinite\nh\u2082 : \u2203 i \u2208 I, a i \u2260 0\n\u22a2 \u2200 (n : \u2115), Odd n \u2192 \u2211 i \u2208 I, a i ^ n = 0"], "t... | false | true | false | 0.2405 |
compfiles_Imo1968P2 | compfiles | Copyright (c) 2023 David Renshaw. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Renshaw
-/
import Mathlib
/-!
# International Mathematical Olympiad 1968, Problem 2
Determine the set of natural numbers x such that
the product of the decimal digits of x is eq... | /- | /-
Copyright (c) 2023 David Renshaw. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Renshaw
-/
import Mathlib
/-!
# International Mathematical Olympiad 1968, Problem 2
Determine the set of natural numbers x such that
the product of the decimal digits of x is... | true | Copyright (c) 2023 David Renshaw. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Renshaw
-/
import Mathlib
/-!
# International Mathematical Olympiad 1968, Problem 2
Determine the set of natural numbers x such that
the product of the decimal digits of x is eq... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo1968P2.lean"} | {"v4.21.0": {"is_valid": true, "has_sorry": false, "errors": [], "timeout_s": 600.0, "latency_s": 0.9052, "verified_at": "2026-03-26T18:16:19.333115+00:00"}} | true | true | false | 0.9052 |
compfiles_Imo1968P3 | compfiles | Copyright (c) 2024 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: John Maar
-/
import Mathlib
/-!
# International Mathematical Olympiad 1968, Problem 3
a, b, c are real with a non-zero. x1, x2, ... , xn satisfy the n equations:
... | /- | /-
Copyright (c) 2024 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: John Maar
-/
import Mathlib
/-!
# International Mathematical Olympiad 1968, Problem 3
a, b, c are real with a non-zero. x1, x2, ... , xn satisfy the n equations:
... | true | Copyright (c) 2024 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: John Maar
-/
import Mathlib
/-!
# International Mathematical Olympiad 1968, Problem 3
a, b, c are real with a non-zero. x1, x2, ... , xn satisfy the n equations:
... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo1968P3.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["function expected at\n sum_sub_distrib\nterm has type\n \u2211 x \u2208 ?m.122615, (?m.122616 x - ?m.122617 x) = \u2211 x \u2208 ?m.122615, ?m.122616 x - \u2211 x \u2208 ?m.122615, ?m.122617 x", "unknown identifier 'mk_set_eq_zero_iff.mpr'", "no goals to... | false | true | false | 3.5939 |
compfiles_Imo1968P5 | compfiles | Copyright (c) 2023 David Renshaw. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Renshaw
-/
import Mathlib
/-!
# International Mathematical Olympiad 1968, Problem 5
Let f be a real-valued function defined for all real numbers x such that,
for some positive c... | /- | /-
Copyright (c) 2023 David Renshaw. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Renshaw
-/
import Mathlib
/-!
# International Mathematical Olympiad 1968, Problem 5
Let f be a real-valued function defined for all real numbers x such that,
for some positiv... | true | Copyright (c) 2023 David Renshaw. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Renshaw
-/
import Mathlib
/-!
# International Mathematical Olympiad 1968, Problem 5
Let f be a real-valued function defined for all real numbers x such that,
for some positive c... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo1968P5.lean"} | {"v4.21.0": {"is_valid": true, "has_sorry": false, "errors": [], "timeout_s": 600.0, "latency_s": 0.9404, "verified_at": "2026-03-26T18:16:20.273627+00:00"}} | true | true | false | 0.9404 |
compfiles_Imo1968P6 | compfiles | Copyright (c) 2026 lean-tom. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: lean-tom (with assistance from Gemini)
-/
import Mathlib
/-!
# International Mathematical Olympiad 1968, Problem 6
For every natural number n, evaluate the sum
∑_{k=0}^{∞} [(n + 2^k) / 2^(k... | /- | /-
Copyright (c) 2026 lean-tom. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: lean-tom (with assistance from Gemini)
-/
import Mathlib
/-!
# International Mathematical Olympiad 1968, Problem 6
For every natural number n, evaluate the sum
∑_{k=0}^{∞} [(n + 2^k) / 2... | true | Copyright (c) 2026 lean-tom. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: lean-tom (with assistance from Gemini)
-/
import Mathlib
/-!
# International Mathematical Olympiad 1968, Problem 6
For every natural number n, evaluate the sum
∑_{k=0}^{∞} [(n + 2^k) / 2^(k... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo1968P6.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["unknown tactic", "unsolved goals\nn k : \u2115\nh_pos : 0 < 2 ^ k\na : \u2115\n\u22a2 (a + 1) / 2 = a - a / 2", "unsolved goals\nn k : \u2115\nh_pos : 0 < 2 ^ k\nidentity : \u2200 (a : \u2115), (a + 1) / 2 = a - a / 2\n\u22a2 (n / 2 ^ k + 1) / 2 = n / 2 ^ ... | false | true | false | 0.1854 |
compfiles_Imo1969P1 | compfiles | Copyright (c) 2020 Kevin Lacker. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Lacker
-/
import Mathlib
/-!
# International Mathematical Olympiad 1969, Problem 1
Prove that there are infinitely many natural numbers a with the following property:
the number z... | /- | /-
Copyright (c) 2020 Kevin Lacker. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Lacker
-/
import Mathlib
/-!
# International Mathematical Olympiad 1969, Problem 1
Prove that there are infinitely many natural numbers a with the following property:
the numbe... | true | Copyright (c) 2020 Kevin Lacker. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Lacker
-/
import Mathlib
/-!
# International Mathematical Olympiad 1969, Problem 1
Prove that there are infinitely many natural numbers a with the following property:
the number z... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo1969P1.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["unknown identifier 'le_natAbs'", "mod_cast has type\n (1 : \u2124) < ?m.11843 : Prop\nbut is expected to have type\n (1 : \u2115) < m.natAbs : Prop", "unknown identifier 'not_prime_of_int_mul'", "unknown tactic", "unsolved goals\nb : \u2115\n\u22a2 1 < 2... | false | true | false | 0.6132 |
compfiles_Imo1969P2 | compfiles | Copyright (c) 2023 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Roozbeh Yousefzadeh
-/
import Mathlib
/-!
# International Mathematical Olympiad 1969, Problem 2
Let a₁, a₂, ..., aₙ be real constants, x be a real variable, and
f(x) =... | /- | /-
Copyright (c) 2023 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Roozbeh Yousefzadeh
-/
import Mathlib
/-!
# International Mathematical Olympiad 1969, Problem 2
Let a₁, a₂, ..., aₙ be real constants, x be a real variable, and
f(x... | true | Copyright (c) 2023 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Roozbeh Yousefzadeh
-/
import Mathlib
/-!
# International Mathematical Olympiad 1969, Problem 2
Let a₁, a₂, ..., aₙ be real constants, x be a real variable, and
f(x) =... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo1969P2.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["`grind` failed\ncase grind.1.2.1.1\nx\u2081 x\u2082 : \u211d\nn : \u2115\na : \u2115 \u2192 \u211d\nf : \u211d \u2192 \u211d\nh\u2081 : \u2200 (x : \u211d), f x = \u2211 i \u2208 Finset.range n, Real.cos (a i + x) / 2 ^ i\nh\u2082 : f x\u2082 = 0\nh\u2083 ... | false | true | false | 4.2314 |
compfiles_Imo1970P3 | compfiles | Copyright (c) 2025 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tomas Ortega
-/
import Mathlib
/-!
# International Mathematical Olympiad 1970, Problem 3
The real numbers a₀, a₁, a₂, ... satisfy 1 = a₀ ≤ a₁ ≤ a₂ ≤ ... . b₁, b₂, b₃, ...... | /- | /-
Copyright (c) 2025 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tomas Ortega
-/
import Mathlib
/-!
# International Mathematical Olympiad 1970, Problem 3
The real numbers a₀, a₁, a₂, ... satisfy 1 = a₀ ≤ a₁ ≤ a₂ ≤ ... . b₁, b₂, b₃, ... | true | Copyright (c) 2025 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tomas Ortega
-/
import Mathlib
/-!
# International Mathematical Olympiad 1970, Problem 3
The real numbers a₀, a₁, a₂, ... satisfy 1 = a₀ ≤ a₁ ≤ a₂ ≤ ... . b₁, b₂, b₃, ...... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo1970P3.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["unknown identifier 'field'", "tactic 'rewrite' failed, did not find instance of the pattern in the target expression\n seq.a (k - 1) / (?m.20018 * seq.a (k - 1))\nseq : IncreasingSequenceFromOne\nk : \u2115\nck_pos : \u2200 (j : \u2115), 0 < c_seq seq j\n... | false | true | false | 4.9862 |
compfiles_Imo1970P4 | compfiles | Copyright (c) 2024 David Renshaw. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Renshaw, Adam Kurkiewicz
-/
import Mathlib
/-!
# International Mathematical Olympiad 1970, Problem 4
Determine the set of all positive integers n with the property that
the set {... | /- | /-
Copyright (c) 2024 David Renshaw. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Renshaw, Adam Kurkiewicz
-/
import Mathlib
/-!
# International Mathematical Olympiad 1970, Problem 4
Determine the set of all positive integers n with the property that
the se... | true | Copyright (c) 2024 David Renshaw. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Renshaw, Adam Kurkiewicz
-/
import Mathlib
/-!
# International Mathematical Olympiad 1970, Problem 4
Determine the set of all positive integers n with the property that
the set {... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo1970P4.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["unknown constant 'Finset.card_filter_add_card_filter_not'", "unknown tactic", "unsolved goals\nx y : \u2115\nx_lt_y : x < y\nclose_by : \u2203 k \u2264 4, x + k = y\nx_div_p : 5 \u2223 x\n\u22a2 \u00ac5 \u2223 y", "unknown tactic", "unsolved goals\ncase h\... | false | true | false | 2.8468 |
compfiles_Imo1970P6 | compfiles | Copyright (c) 2024 David Renshaw. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Renshaw
-/
import Mathlib
/-!
# International Mathematical Olympiad 1970, Problem 6
In a plane there are 100 points, no three of which are collinear.
Consider all possible trian... | /- | /-
Copyright (c) 2024 David Renshaw. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Renshaw
-/
import Mathlib
/-!
# International Mathematical Olympiad 1970, Problem 6
In a plane there are 100 points, no three of which are collinear.
Consider all possible tr... | false | null | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo1970P6.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": true, "errors": [], "timeout_s": 600.0, "latency_s": 0.253, "verified_at": "2026-03-26T18:16:22.515581+00:00"}} | false | true | true | 0.253 |
compfiles_Imo1971P1 | compfiles | Copyright (c) 2024 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Francesco Cappetti
-/
import Mathlib
/-!
# International Mathematical Olympiad 1971, Problem 1
Prove that the following assertion is true for n = 3 and n = 5, and that it... | /- | /-
Copyright (c) 2024 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Francesco Cappetti
-/
import Mathlib
/-!
# International Mathematical Olympiad 1971, Problem 1
Prove that the following assertion is true for n = 3 and n = 5, and that... | true | Copyright (c) 2024 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Francesco Cappetti
-/
import Mathlib
/-!
# International Mathematical Olympiad 1971, Problem 1
Prove that the following assertion is true for n = 3 and n = 5, and that it... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo1971P1.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["`grind` failed\ncase grind.2.1.1.1\nn : \u2115\ni : Fin n\na : Fin n \u2192 \u211d\nh : \u00ac\u220f j \u2208 Finset.univ.erase i, (a i - a j) = 1 * \u220f x \u2208 Finset.univ.erase i, if x = i then 1 else a i - a x\nh_1 : \u00ac(fun x => if x = i then 1 ... | false | true | false | 0.8554 |
compfiles_Imo1971P3 | compfiles | Copyright (c) 2024 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: InternLM-MATH LEAN Formalizer v0.1, Constantin Seebach
-/
import Mathlib
/-!
# International Mathematical Olympiad 1971, Problem 3
Prove that we can find an infinite set ... | /- | /-
Copyright (c) 2024 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: InternLM-MATH LEAN Formalizer v0.1, Constantin Seebach
-/
import Mathlib
/-!
# International Mathematical Olympiad 1971, Problem 3
Prove that we can find an infinite s... | true | Copyright (c) 2024 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: InternLM-MATH LEAN Formalizer v0.1, Constantin Seebach
-/
import Mathlib
/-!
# International Mathematical Olympiad 1971, Problem 3
Prove that we can find an infinite set ... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo1971P3.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["unknown tactic", "unknown constant 'Nat.clog_le_iff_le_pow'", "no goals to be solved", "unsolved goals\nn : \u2115\nih : 3 \u2264 a n \u2227 Odd (2 ^ a n - 3)\nh : 3 \u2264 2 ^ (a n * \u220f p \u2208 (2 ^ a n - 3).primeFactors, (p - 1))\n\u22a2 1 \u2264 \u... | false | true | false | 1.2488 |
compfiles_Imo1971P5 | compfiles | Copyright (c) 2024 David Renshaw. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Renshaw, Benpigchu
-/
import Mathlib
/-!
# International Mathematical Olympiad 1971, Problem 5
Prove that for every natural number m there exists a nonempty finite
set S of poin... | /- | /-
Copyright (c) 2024 David Renshaw. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Renshaw, Benpigchu
-/
import Mathlib
/-!
# International Mathematical Olympiad 1971, Problem 5
Prove that for every natural number m there exists a nonempty finite
set S of p... | true | Copyright (c) 2024 David Renshaw. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Renshaw, Benpigchu
-/
import Mathlib
/-!
# International Mathematical Olympiad 1971, Problem 5
Prove that for every natural number m there exists a nonempty finite
set S of poin... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo1971P5.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["unknown constant 'PiLp.norm_single'", "unknown constant 'PiLp.norm_single'", "unknown tactic", "unsolved goals\nS : Set Pt\nhS : S.Finite\nh' :\n {p | \u2203 s t, s \u2208 S \u2227 t \u2208 S \u2227 s \u2260 t \u2227 \u2016p\u2016 = 1 \u2227 dist s (t + p... | false | true | false | 3.3947 |
compfiles_Imo1971P6 | compfiles | Copyright (c) 2026 lean-tom. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: lean-tom (with assistance from Gemini)
-/
import Mathlib
/-!
# International Mathematical Olympiad 1971, Problem 6
Let $A = (a_{ij})$ be an $n \times n$ matrix with non-negative integer ent... | /- | /-
Copyright (c) 2026 lean-tom. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: lean-tom (with assistance from Gemini)
-/
import Mathlib
/-!
# International Mathematical Olympiad 1971, Problem 6
Let $A = (a_{ij})$ be an $n \times n$ matrix with non-negative integer ... | true | Copyright (c) 2026 lean-tom. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: lean-tom (with assistance from Gemini)
-/
import Mathlib
/-!
# International Mathematical Olympiad 1971, Problem 6
Let $A = (a_{ij})$ be an $n \times n$ matrix with non-negative integer ent... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo1971P6.lean"} | {"v4.21.0": {"is_valid": true, "has_sorry": false, "errors": [], "timeout_s": 120, "latency_s": 4.8352, "verified_at": "2026-03-30T14:39:40.328236+00:00"}} | true | true | false | 4.8352 |
compfiles_Imo1972P1 | compfiles | Copyright (c) 2024 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Renshaw
-/
import Mathlib
/-!
# International Mathematical Olympiad 1972, Problem 1
Prove that from a set of ten distinct two-digit numbers (in
decimal), it is poss... | /- | /-
Copyright (c) 2024 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Renshaw
-/
import Mathlib
/-!
# International Mathematical Olympiad 1972, Problem 1
Prove that from a set of ten distinct two-digit numbers (in
decimal), it is p... | true | Copyright (c) 2024 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Renshaw
-/
import Mathlib
/-!
# International Mathematical Olympiad 1972, Problem 1
Prove that from a set of ten distinct two-digit numbers (in
decimal), it is poss... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo1972P1.lean"} | {"v4.21.0": {"is_valid": true, "has_sorry": false, "errors": [], "timeout_s": 120, "latency_s": 0.6073, "verified_at": "2026-03-30T14:39:45.163583+00:00"}} | true | true | false | 0.6073 |
compfiles_Imo1972P3 | compfiles | Copyright (c) 2024 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Hongyu Ouyang
-/
import Mathlib
/-!
# International Mathematical Olympiad 1972, Problem 3
Let m and n be non-negative integers. Prove that
(2m)!(2n)! / (m!n!(m + n)... | /- | /-
Copyright (c) 2024 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Hongyu Ouyang
-/
import Mathlib
/-!
# International Mathematical Olympiad 1972, Problem 3
Let m and n be non-negative integers. Prove that
(2m)!(2n)! / (m!n!(m +... | true | Copyright (c) 2024 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Hongyu Ouyang
-/
import Mathlib
/-!
# International Mathematical Olympiad 1972, Problem 3
Let m and n be non-negative integers. Prove that
(2m)!(2n)! / (m!n!(m + n)... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo1972P3.lean"} | {"v4.21.0": {"is_valid": true, "has_sorry": false, "errors": [], "timeout_s": 120, "latency_s": 1.3442, "verified_at": "2026-03-30T14:39:45.770931+00:00"}} | true | true | false | 1.3442 |
compfiles_Imo1972P4 | compfiles | Copyright (c) 2024 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: InternLM-MATH LEAN Formalizer v0.1, Maximiliano Onofre-Martínez
-/
import Mathlib
/-!
# International Mathematical Olympiad 1972, Problem 4
Find all positive real solutio... | /- | /-
Copyright (c) 2024 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: InternLM-MATH LEAN Formalizer v0.1, Maximiliano Onofre-Martínez
-/
import Mathlib
/-!
# International Mathematical Olympiad 1972, Problem 4
Find all positive real solu... | true | Copyright (c) 2024 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: InternLM-MATH LEAN Formalizer v0.1, Maximiliano Onofre-Martínez
-/
import Mathlib
/-!
# International Mathematical Olympiad 1972, Problem 4
Find all positive real solutio... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo1972P4.lean"} | {"v4.21.0": {"is_valid": true, "has_sorry": false, "errors": [], "timeout_s": 600.0, "latency_s": 2.4445, "verified_at": "2026-03-26T18:16:29.330031+00:00"}} | true | true | false | 2.4445 |
compfiles_Imo1972P5 | compfiles | Copyright (c) 2020 Ruben Van de Velde, Stanislas Polu. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ruben Van de Velde, Stanislas Polu
-/
import Mathlib
/-!
# International Mathematical Olympiad 1972, Problem 5
`f` and `g` are real-valued functions defined on the... | /- | /-
Copyright (c) 2020 Ruben Van de Velde, Stanislas Polu. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ruben Van de Velde, Stanislas Polu
-/
import Mathlib
/-!
# International Mathematical Olympiad 1972, Problem 5
`f` and `g` are real-valued functions defined on ... | true | Copyright (c) 2020 Ruben Van de Velde, Stanislas Polu. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ruben Van de Velde, Stanislas Polu
-/
import Mathlib
/-!
# International Mathematical Olympiad 1972, Problem 5
`f` and `g` are real-valued functions defined on the... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo1972P5.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["unknown identifier 'mul_le_mul_iff_right\u2080'", "unsolved goals\nf g : \u211d \u2192 \u211d\nhf1 : \u2200 (x y : \u211d), f (x + y) + f (x - y) = 2 * f x * g y\nhf2 : BddAbove (Set.range fun x => \u2016f x\u2016)\ny : \u211d\nH : 1 < \u2016g y\u2016\nx\u... | false | true | false | 0.3392 |
compfiles_Imo1973P3 | compfiles | Copyright (c) 2025 Roozbeh Yousefzadeh. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Roozbeh Yousefzadeh
-/
import Mathlib
/-!
# International Mathematical Olympiad 1973, Problem 3
Let $a$ and $b$ be real numbers for which the equation
$x^4 + ax^3 + bx^2 + ax + ... | /- | /-
Copyright (c) 2025 Roozbeh Yousefzadeh. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Roozbeh Yousefzadeh
-/
import Mathlib
/-!
# International Mathematical Olympiad 1973, Problem 3
Let $a$ and $b$ be real numbers for which the equation
$x^4 + ax^3 + bx^2 + ax... | true | Copyright (c) 2025 Roozbeh Yousefzadeh. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Roozbeh Yousefzadeh
-/
import Mathlib
/-!
# International Mathematical Olympiad 1973, Problem 3
Let $a$ and $b$ be real numbers for which the equation
$x^4 + ax^3 + bx^2 + ax + ... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo1973P3.lean"} | {"v4.21.0": {"is_valid": true, "has_sorry": false, "errors": [], "timeout_s": 600.0, "latency_s": 3.7796, "verified_at": "2026-03-26T18:16:30.740374+00:00"}} | true | true | false | 3.7796 |
compfiles_Imo1973P5 | compfiles | Copyright (c) 2024 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: InternLM-MATH LEAN Formalizer v0.1 , Shahar Blumentzvaig
-/
import Mathlib
/-!
# International Mathematical Olympiad 1973, Problem 5
$G$ is a set of non-constant functions... | /- | /-
Copyright (c) 2024 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: InternLM-MATH LEAN Formalizer v0.1 , Shahar Blumentzvaig
-/
import Mathlib
/-!
# International Mathematical Olympiad 1973, Problem 5
$G$ is a set of non-constant functi... | true | Copyright (c) 2024 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: InternLM-MATH LEAN Formalizer v0.1 , Shahar Blumentzvaig
-/
import Mathlib
/-!
# International Mathematical Olympiad 1973, Problem 5
$G$ is a set of non-constant functions... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo1973P5.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["`grind` failed\ncase grind\nG : Set (\u211d \u2192 \u211d)\nhf : \u2200 f \u2208 G, \u2203 a, \u00aca = 0 \u2227 \u2203 x, \u2200 (x_1 : \u211d), f x_1 = a * x_1 + x\nhG : \u2200 f \u2208 G, \u2200 g \u2208 G, g \u2218 f \u2208 G\nhinv : \u2200 f \u2208 G,... | false | true | false | 14.2919 |
compfiles_Imo1973P6 | compfiles | Copyright (c) 2026 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Constantin Seebach
-/
import Mathlib
/-!
# International Mathematical Olympiad 1973, Problem 6
Let $a_1, a_2,\cdots, a_n$ be $n$ positive numbers,
and let $q$ be a given ... | /- | /-
Copyright (c) 2026 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Constantin Seebach
-/
import Mathlib
/-!
# International Mathematical Olympiad 1973, Problem 6
Let $a_1, a_2,\cdots, a_n$ be $n$ positive numbers,
and let $q$ be a giv... | true | Copyright (c) 2026 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Constantin Seebach
-/
import Mathlib
/-!
# International Mathematical Olympiad 1973, Problem 6
Let $a_1, a_2,\cdots, a_n$ be $n$ positive numbers,
and let $q$ be a given ... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo1973P6.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["unknown tactic", "unsolved goals\nn : \u2115\na : Fin n \u2192 \u211d\nq : \u211d\nk : \u2115\nx\u271d : k + 1 < n\nj : ?m.3029\nhq : q \u2208 Set.Ioo 0 1\nf : \u211d\n\u22a2 k + 1 < n", "unknown tactic", "unsolved goals\nn : \u2115\na : Fin n \u2192 \u211... | false | true | false | 0.2104 |
compfiles_Imo1974P1 | compfiles | Copyright (c) 2025 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Lynn Van Hauwe
-/
import Mathlib
/-!
# International Mathematical Olympiad 1974, Problem 1
Three players $A, B$ and $C$ play the following game:
* On each of three card... | /- | /-
Copyright (c) 2025 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Lynn Van Hauwe
-/
import Mathlib
/-!
# International Mathematical Olympiad 1974, Problem 1
Three players $A, B$ and $C$ play the following game:
* On each of three c... | true | Copyright (c) 2025 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Lynn Van Hauwe
-/
import Mathlib
/-!
# International Mathematical Olympiad 1974, Problem 1
Three players $A, B$ and $C$ play the following game:
* On each of three card... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo1974P1.lean"} | {"v4.21.0": {"is_valid": true, "has_sorry": false, "errors": [], "timeout_s": 120, "latency_s": 2.4928, "verified_at": "2026-03-30T14:40:11.159523+00:00"}} | true | true | false | 2.4928 |
compfiles_Imo1974P3 | compfiles | Copyright (c) 2025 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Roozbeh Yousefzadeh
-/
import Mathlib
/-!
# International Mathematical Olympiad 1974, Problem 3
Prove that the sum from k = 0 to n inclusive of
Choose[2n + 1, 2k + 1] ... | /- | /-
Copyright (c) 2025 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Roozbeh Yousefzadeh
-/
import Mathlib
/-!
# International Mathematical Olympiad 1974, Problem 3
Prove that the sum from k = 0 to n inclusive of
Choose[2n + 1, 2k + ... | true | Copyright (c) 2025 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Roozbeh Yousefzadeh
-/
import Mathlib
/-!
# International Mathematical Olympiad 1974, Problem 3
Prove that the sum from k = 0 to n inclusive of
Choose[2n + 1, 2k + 1] ... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo1974P3.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["unknown tactic", "unsolved goals\nn : \u2115\nk : \u211d\nf : \u2115 \u2192 \u211d := fun i => \u2191((2 * n + 1).choose i) * k ^ i\nfs\u2082 : Finset \u2115 := Finset.range (2 * n + 2)\nfs\u2080 : Finset \u2115 := {x \u2208 fs\u2082 | Odd x}\nfs\u2081 : F... | false | true | false | 3.6842 |
compfiles_Imo1974P5 | compfiles | Copyright (c) 2023 David Renshaw. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Renshaw
-/
import Mathlib
/-!
# International Mathematical Olympiad 1974, Problem 5
What are the possible values of
a / (a + b + d) + b / (a + b + c) + c / (b + c + d) + d / (... | /- | /-
Copyright (c) 2023 David Renshaw. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Renshaw
-/
import Mathlib
/-!
# International Mathematical Olympiad 1974, Problem 5
What are the possible values of
a / (a + b + d) + b / (a + b + c) + c / (b + c + d) + d ... | true | Copyright (c) 2023 David Renshaw. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Renshaw
-/
import Mathlib
/-!
# International Mathematical Olympiad 1974, Problem 5
What are the possible values of
a / (a + b + d) + b / (a + b + c) + c / (b + c + d) + d / (... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo1974P5.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["unknown tactic", "unsolved goals\na b c d : \u211d\nha : 0 < a\nhb : 0 < b\nhc : 0 < c\nhd : 0 < d\nh3 : a / (a + b + d) < a / (a + b)\nh4 : b / (a + b + c) < b / (a + b)\nh5 : c / (b + c + d) < c / (c + d)\nh6 : d / (a + c + d) < d / (c + d)\n\u22a2 a / (... | false | true | false | 2.4046 |
compfiles_Imo1975P1 | compfiles | Copyright (c) 2022 Mantas Bakšys. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mantas Bakšys
-/
import Mathlib
/-!
# International Mathematical Olympiad 1975, Problem 1
Let `x₁, x₂, ... , xₙ` and `y₁, y₂, ... , yₙ` be two sequences of real numbers, such that
`x₁ ... | /- | /-
Copyright (c) 2022 Mantas Bakšys. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mantas Bakšys
-/
import Mathlib
/-!
# International Mathematical Olympiad 1975, Problem 1
Let `x₁, x₂, ... , xₙ` and `y₁, y₂, ... , yₙ` be two sequences of real numbers, such that
`... | true | Copyright (c) 2022 Mantas Bakšys. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mantas Bakšys
-/
import Mathlib
/-!
# International Mathematical Olympiad 1975, Problem 1
Let `x₁, x₂, ... , xₙ` and `y₁, y₂, ... , yₙ` be two sequences of real numbers, such that
`x₁ ... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo1975P1.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["unknown identifier 'mul_le_mul_iff_right\u2080'", "tactic 'apply' failed, could not unify the type of `MonovaryOn.sum_mul_comp_perm_le_sum_mul ?m.8124 h\u03c3`\n \u2211 i \u2208 Finset.Icc 1 n, ?m.8122 i * ?m.8123 (\u03c3 i) \u2264 \u2211 i \u2208 Finset.... | false | true | false | 0.232 |
compfiles_Imo1975P2 | compfiles | Copyright (c) 2024 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: InternLM-MATH LEAN Formalizer v0.1, Shahar Blumentzvaig
-/
import Mathlib
/-!
# International Mathematical Olympiad 1975, Problem 2
Let a1 < a2 < a3 < ... be positive in... | /- | /-
Copyright (c) 2024 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: InternLM-MATH LEAN Formalizer v0.1, Shahar Blumentzvaig
-/
import Mathlib
/-!
# International Mathematical Olympiad 1975, Problem 2
Let a1 < a2 < a3 < ... be positive... | true | Copyright (c) 2024 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: InternLM-MATH LEAN Formalizer v0.1, Shahar Blumentzvaig
-/
import Mathlib
/-!
# International Mathematical Olympiad 1975, Problem 2
Let a1 < a2 < a3 < ... be positive in... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo1975P2.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["unknown tactic", "unsolved goals\na : \u2115 \u2192 \u2124\napos : \u2200 (i : \u2115), 0 < a i\nha : \u2200 (i : \u2115), a i < a (i + 1)\nb : \u2115 \u2192 \u2115 := fun n => (a n).natAbs\ni : \u2115\nhn0 : \u2200 (j : \u2115), a j \u2260 0\nn0 : \u2115\... | false | true | false | 0.2735 |
compfiles_Imo1975P4 | compfiles | Copyright (c) 2026 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Constantin Seebach
-/
import Mathlib
/-!
# International Mathematical Olympiad 1975, Problem 4
When $4444^{4444}$ is written in decimal notation, the sum of its digits is... | /- | /-
Copyright (c) 2026 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Constantin Seebach
-/
import Mathlib
/-!
# International Mathematical Olympiad 1975, Problem 4
When $4444^{4444}$ is written in decimal notation, the sum of its digits... | true | Copyright (c) 2026 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Constantin Seebach
-/
import Mathlib
/-!
# International Mathematical Olympiad 1975, Problem 4
When $4444^{4444}$ is written in decimal notation, the sum of its digits is... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo1975P4.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["unknown constant 'Nat.length_digits'", "unsolved goals\nn b : \u2115\nhn : n \u2260 0\nhb : 1 < b\n\u22a2 (b.digits n).sum \u2264 (Nat.log b n + 1) * (b - 1)", "unknown tactic", "unknown identifier 'mul_le_mul_iff_left\u2080'", "unknown constant 'Nat.clog_... | false | true | false | 0.4098 |
compfiles_Imo1975P5 | compfiles | Copyright (c) 2026 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Constantin Seebach
-/
import Mathlib
/-!
# International Mathematical Olympiad 1975, Problem 5
Determine, with proof, whether or not one can find $1975$ points on the cir... | /- | /-
Copyright (c) 2026 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Constantin Seebach
-/
import Mathlib
/-!
# International Mathematical Olympiad 1975, Problem 5
Determine, with proof, whether or not one can find $1975$ points on the ... | true | Copyright (c) 2026 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Constantin Seebach
-/
import Mathlib
/-!
# International Mathematical Olympiad 1975, Problem 5
Determine, with proof, whether or not one can find $1975$ points on the cir... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo1975P5.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["unknown tactic", "unsolved goals\n\u22a2 \u221a(1 - (4 / 5) ^ 2) = \u2191(3 / 5)", "`grind` failed\ncase grind\nn : \u2115\nleft : \u00acIrrational (Real.sin (\u03b8 * \u2191n))\nright : \u00acIrrational (Real.cos (\u03b8 * \u2191n))\nh :\n Irrational (Re... | false | true | false | 0.6696 |
compfiles_Imo1976P2 | compfiles | Copyright (c) 2026 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Constantin Seebach
-/
import Mathlib
/-!
# International Mathematical Olympiad 1976, Problem 2
Let $P_{1}(x) = x^{2} - 2$ and $P_{j}(x) = P_{1}(P_{j - 1}(x))$ for $j= 2,\... | /- | /-
Copyright (c) 2026 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Constantin Seebach
-/
import Mathlib
/-!
# International Mathematical Olympiad 1976, Problem 2
Let $P_{1}(x) = x^{2} - 2$ and $P_{j}(x) = P_{1}(P_{j - 1}(x))$ for $j= ... | true | Copyright (c) 2026 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Constantin Seebach
-/
import Mathlib
/-!
# International Mathematical Olympiad 1976, Problem 2
Let $P_{1}(x) = x^{2} - 2$ and $P_{j}(x) = P_{1}(P_{j - 1}(x))$ for $j= 2,\... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo1976P2.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["unknown constant 'IsAlgClosed.card_aroots_eq_natDegree'", "failed to synthesize\n ZeroLEOneClass \u03b4\n\nAdditional diagnostic information may be available using the `set_option diagnostics true` command.", "failed to synthesize\n ZeroLEOneClass \u03b4... | false | true | false | 5.0178 |
compfiles_Imo1976P4 | compfiles | Copyright (c) 2024 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Benpigchu
-/
import Mathlib
/-!
# International Mathematical Olympiad 1976, Problem 4
Determine, with proof, the largest number which is the product
of positive integers ... | /- | /-
Copyright (c) 2024 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Benpigchu
-/
import Mathlib
/-!
# International Mathematical Olympiad 1976, Problem 4
Determine, with proof, the largest number which is the product
of positive intege... | true | Copyright (c) 2024 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Benpigchu
-/
import Mathlib
/-!
# International Mathematical Olympiad 1976, Problem 4
Determine, with proof, the largest number which is the product
of positive integers ... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo1976P4.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["function expected at\n mul_le_mul_right ?m.33970\nterm has type\n ?m.33167 * ?m.33166 \u2264 ?m.33168 * ?m.33166 \u2194 ?m.33167 \u2264 ?m.33168", "function expected at\n mul_le_mul_left ?m.36254\nterm has type\n ?m.35448 * ?m.35449 \u2264 ?m.35448 * ?... | false | true | false | 2.0615 |
compfiles_Imo1976P6 | compfiles | Copyright (c) 2024 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: InternLM-MATH LEAN Formalizer v0.1, Aristotle-Harmonic, David Renshaw
-/
import Mathlib
/-!
# International Mathematical Olympiad 1976, Problem 6
The sequence u_0, u_1, u... | /- | /-
Copyright (c) 2024 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: InternLM-MATH LEAN Formalizer v0.1, Aristotle-Harmonic, David Renshaw
-/
import Mathlib
/-!
# International Mathematical Olympiad 1976, Problem 6
The sequence u_0, u_1... | true | Copyright (c) 2024 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: InternLM-MATH LEAN Formalizer v0.1, Aristotle-Harmonic, David Renshaw
-/
import Mathlib
/-!
# International Mathematical Olympiad 1976, Problem 6
The sequence u_0, u_1, u... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo1976P6.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["unknown tactic"], "timeout_s": 600.0, "latency_s": 0.0767, "verified_at": "2026-03-26T18:16:41.346100+00:00"}} | false | true | false | 0.0767 |
compfiles_Imo1977P2 | compfiles | Copyright (c) 2026 Constantin Seebach. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Constantin Seebach
-/
import Mathlib
/-!
# International Mathematical Olympiad 1977, Problem 2
In a finite sequence of real numbers the sum of any seven successive terms is negat... | /- | /-
Copyright (c) 2026 Constantin Seebach. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Constantin Seebach
-/
import Mathlib
/-!
# International Mathematical Olympiad 1977, Problem 2
In a finite sequence of real numbers the sum of any seven successive terms is ne... | true | Copyright (c) 2026 Constantin Seebach. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Constantin Seebach
-/
import Mathlib
/-!
# International Mathematical Olympiad 1977, Problem 2
In a finite sequence of real numbers the sum of any seven successive terms is negat... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo1977P2.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["unknown tactic", "unsolved goals\nn : \u2115\nngt : max_num_terms < n\nthis : NeZero n\nx : Fin n \u2192 \u211d\nc :\n \u2200 (x_1 : Fin n),\n (\u2200 (h7 : \u2191x_1 + 6 < n), sum_successive_terms x x_1 7 h7 < 0) \u2227\n \u2200 (h : \u2191x_1 + ... | false | true | false | 1.0745 |
compfiles_Imo1977P4 | compfiles | Copyright (c) 2024 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: InternLM-MATH LEAN Formalizer v0.1, Goedel-Prover-V2
-/
import Mathlib
/-!
# International Mathematical Olympiad 1977, Problem 4
Define f(x) = 1 - a cos x - b sin x - A c... | /- | /-
Copyright (c) 2024 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: InternLM-MATH LEAN Formalizer v0.1, Goedel-Prover-V2
-/
import Mathlib
/-!
# International Mathematical Olympiad 1977, Problem 4
Define f(x) = 1 - a cos x - b sin x - ... | true | Copyright (c) 2024 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: InternLM-MATH LEAN Formalizer v0.1, Goedel-Prover-V2
-/
import Mathlib
/-!
# International Mathematical Olympiad 1977, Problem 4
Define f(x) = 1 - a cos x - b sin x - A c... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo1977P4.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["unknown tactic", "unsolved goals\nf : \u211d \u2192 \u211d\na b A B : \u211d\nh\u2080 : \u2200 (x : \u211d), f x = 1 - a * Real.cos x - b * Real.sin x - A * Real.cos (2 * x) - B * Real.sin (2 * x)\nh\u2081 : \u2200 (x : \u211d), f x \u2265 0\nh : 1 < A ^ 2... | false | true | false | 2.9583 |
compfiles_Imo1977P5 | compfiles | Copyright (c) 2025 Roozbeh Yousefzadeh. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Roozbeh Yousefzadeh
-/
import Mathlib
/-!
# International Mathematical Olympiad 1977, Problem 5
Let $a,b$ be two natural numbers. When we divide $a^2+b^2$ by $a+b$,
we get the r... | /- | /-
Copyright (c) 2025 Roozbeh Yousefzadeh. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Roozbeh Yousefzadeh
-/
import Mathlib
/-!
# International Mathematical Olympiad 1977, Problem 5
Let $a,b$ be two natural numbers. When we divide $a^2+b^2$ by $a+b$,
we get th... | true | Copyright (c) 2025 Roozbeh Yousefzadeh. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Roozbeh Yousefzadeh
-/
import Mathlib
/-!
# International Mathematical Olympiad 1977, Problem 5
Let $a,b$ be two natural numbers. When we divide $a^2+b^2$ by $a+b$,
we get the r... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo1977P5.lean"} | {"v4.21.0": {"is_valid": true, "has_sorry": false, "errors": [], "timeout_s": 120, "latency_s": 6.7109, "verified_at": "2026-03-30T14:40:51.112455+00:00"}} | true | true | false | 6.7109 |
compfiles_Imo1977P6 | compfiles | Copyright (c) 2021 Tian Chen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tian Chen
-/
import Mathlib
/-!
# International Mathematical Olympiad 1977, Problem 6
Suppose `f : ℕ+ → ℕ+` satisfies `f(f(n)) < f(n + 1)` for all `n`.
Prove that `f(n) = n` for all `n`.
-... | /- | /-
Copyright (c) 2021 Tian Chen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tian Chen
-/
import Mathlib
/-!
# International Mathematical Olympiad 1977, Problem 6
Suppose `f : ℕ+ → ℕ+` satisfies `f(f(n)) < f(n + 1)` for all `n`.
Prove that `f(n) = n` for all `n`... | true | Copyright (c) 2021 Tian Chen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tian Chen
-/
import Mathlib
/-!
# International Mathematical Olympiad 1977, Problem 6
Suppose `f : ℕ+ → ℕ+` satisfies `f(f(n)) < f(n + 1)` for all `n`.
Prove that `f(n) = n` for all `n`.
-... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo1977P6.lean"} | {"v4.21.0": {"is_valid": true, "has_sorry": false, "errors": [], "timeout_s": 600.0, "latency_s": 0.2406, "verified_at": "2026-03-26T18:16:41.586816+00:00"}} | true | true | false | 0.2406 |
compfiles_Imo1978P1 | compfiles | Copyright (c) 2024 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: InternLM-MATH LEAN Formalizer v0.1, David Renshaw
-/
import Mathlib
/-!
# International Mathematical Olympiad 1978, Problem 1
m and n are positive integers with m < n.
Th... | /- | /-
Copyright (c) 2024 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: InternLM-MATH LEAN Formalizer v0.1, David Renshaw
-/
import Mathlib
/-!
# International Mathematical Olympiad 1978, Problem 1
m and n are positive integers with m < n.... | true | Copyright (c) 2024 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: InternLM-MATH LEAN Formalizer v0.1, David Renshaw
-/
import Mathlib
/-!
# International Mathematical Olympiad 1978, Problem 1
m and n are positive integers with m < n.
Th... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo1978P1.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["unknown tactic", "unsolved goals\nm n : \u2115\nhmn : (m, n) = solution\nm' n' : \u2115\nh1 : 1 \u2264 m'\nh2 : m' < n'\nh3 : 8 * 125 \u2223 1978 ^ m' * (1978 ^ (n' - m') - 1)\nh4 : 8 \u2223 1978 ^ m'\nh5 : 3 \u2264 m'\n\u22a2 m' - 3 + 3 = m'", "unsolved g... | false | true | false | 0.6238 |
compfiles_Imo1978P5 | compfiles | Copyright (c) 2025 Roozbeh Yousefzadeh. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Roozbeh Yousefzadeh
-/
import Mathlib
/-!
# International Mathematical Olympiad 1978, Problem 5
Let a_k be a sequence of distinct positive integers for k = 1,2,3, ...
Prove th... | /- | /-
Copyright (c) 2025 Roozbeh Yousefzadeh. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Roozbeh Yousefzadeh
-/
import Mathlib
/-!
# International Mathematical Olympiad 1978, Problem 5
Let a_k be a sequence of distinct positive integers for k = 1,2,3, ...
Prove... | true | Copyright (c) 2025 Roozbeh Yousefzadeh. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Roozbeh Yousefzadeh
-/
import Mathlib
/-!
# International Mathematical Olympiad 1978, Problem 5
Let a_k be a sequence of distinct positive integers for k = 1,2,3, ...
Prove th... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo1978P5.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["unknown tactic", "unknown identifier 'Icc'", "unknown identifier 'Icc'", "unknown identifier 'Icc'", "unknown identifier 'Icc'", "unknown identifier 'Icc'", "unsolved goals\ncase refine_1\nn : \u2115\nf : \u2115 \u2192 \u2115\nh\u2080 : \u2200 (m : \u2115)... | false | true | false | 0.592 |
compfiles_Imo1978P6 | compfiles | Copyright (c) 2025 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: InternLM-MATH LEAN Formalizer v0.1, Constantin Seebach
-/
import Mathlib
/-!
# International Mathematical Olympiad 1978, Problem 6
An international society has its member... | /- | /-
Copyright (c) 2025 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: InternLM-MATH LEAN Formalizer v0.1, Constantin Seebach
-/
import Mathlib
/-!
# International Mathematical Olympiad 1978, Problem 6
An international society has its mem... | true | Copyright (c) 2025 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: InternLM-MATH LEAN Formalizer v0.1, Constantin Seebach
-/
import Mathlib
/-!
# International Mathematical Olympiad 1978, Problem 6
An international society has its member... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo1978P6.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["unexpected token '.'; expected ']'", "unexpected token '!'; expected ']'", "`grind` failed\ncase grind\nM N : \u2115\nC : { x // x \u2208 Finset.Icc 1 M } \u2192 Fin N\ninst : NeZero N\nh : \u2200 (j i k : { x // x \u2208 Finset.Icc 1 M }), C i = C j \u219... | false | true | false | 3.5573 |
compfiles_Imo1979P1 | compfiles | Copyright (c) 2023 David Renshaw. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Renshaw
-/
import Mathlib
/-!
# International Mathematical Olympiad 1979, Problem 1
Suppose that p and q are positive integers such that
p / q = 1 - 1/2 + 1/3 - 1/4 + ... - 1... | /- | /-
Copyright (c) 2023 David Renshaw. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Renshaw
-/
import Mathlib
/-!
# International Mathematical Olympiad 1979, Problem 1
Suppose that p and q are positive integers such that
p / q = 1 - 1/2 + 1/3 - 1/4 + ... ... | true | Copyright (c) 2023 David Renshaw. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Renshaw
-/
import Mathlib
/-!
# International Mathematical Olympiad 1979, Problem 1
Suppose that p and q are positive integers such that
p / q = 1 - 1/2 + 1/3 - 1/4 + ... - 1... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo1979P1.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["unknown tactic", "unsolved goals\nh2 :\n \u2211 x \u2208 Finset.range 1319with Even x, 1 / (\u2191x + 1) + \u2211 x \u2208 Finset.range 1319with \u00acEven x, 1 / (\u2191x + 1) =\n \u2211 x \u2208 Finset.range 1319, 1 / (\u2191x + 1)\na b : \u2115\nhab... | false | true | false | 0.7497 |
compfiles_Imo1979P5 | compfiles | Copyright (c) 2024 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: InternLM-MATH LEAN Formalizer v0.1, Maximiliano Onofre-Martínez
-/
import Mathlib
/-!
# International Mathematical Olympiad 1979, Problem 5
Find all real numbers a for wh... | /- | /-
Copyright (c) 2024 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: InternLM-MATH LEAN Formalizer v0.1, Maximiliano Onofre-Martínez
-/
import Mathlib
/-!
# International Mathematical Olympiad 1979, Problem 5
Find all real numbers a for... | true | Copyright (c) 2024 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: InternLM-MATH LEAN Formalizer v0.1, Maximiliano Onofre-Martínez
-/
import Mathlib
/-!
# International Mathematical Olympiad 1979, Problem 5
Find all real numbers a for wh... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo1979P5.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["`grind` failed\ncase grind\na x1 x2 x3 x4 x5 : \u211d\nhx1 : 0 \u2264 x1\nhx2 : 0 \u2264 x2\nhx3 : 0 \u2264 x3\nhx4 : 0 \u2264 x4\nhx5 : 0 \u2264 x5\nh\u2081 : x1 + 2 * x2 + 3 * x3 + 4 * x4 + 5 * x5 = a\nh\u2082 : x1 + 2 ^ 3 * x2 + 3 ^ 3 * x3 + 4 ^ 3 * x4 ... | false | true | false | 2.2811 |
compfiles_Imo1979P6 | compfiles | Copyright (c) 2026 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Constantin Seebach
-/
import Mathlib
/-!
# International Mathematical Olympiad 1979, Problem 6
Let $A$ and $E$ be opposite vertices of an octagon.
A frog starts at vertex... | /- | /-
Copyright (c) 2026 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Constantin Seebach
-/
import Mathlib
/-!
# International Mathematical Olympiad 1979, Problem 6
Let $A$ and $E$ be opposite vertices of an octagon.
A frog starts at ver... | true | Copyright (c) 2026 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Constantin Seebach
-/
import Mathlib
/-!
# International Mathematical Olympiad 1979, Problem 6
Let $A$ and $E$ be opposite vertices of an octagon.
A frog starts at vertex... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo1979P6.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["`grind` failed\ncase grind\n\u03b1 : Type\ninst : (a b : \u03b1) \u2192 Decidable (a = b)\np q : \u03b1 \u2192 Prop\ninst_1 : Fintype (Subtype p)\ninst_2 : (a : \u03b1) \u2192 Decidable (q a)\nval_1 : \u03b1\nproperty : p val_1\nproperty_1 : \u27e8val_1, \... | false | true | false | 2.319 |
compfiles_Imo1981P2 | compfiles | Copyright (c) 2026 Constantin Seebach. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Constantin Seebach
-/
import Mathlib
namespace Imo1981P2
/-!
# International Mathematical Olympiad 1981, Problem 2
Let $1 \le r \le n$ and consider all subsets of $r$ elements of... | /- | /-
Copyright (c) 2026 Constantin Seebach. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Constantin Seebach
-/
import Mathlib
namespace Imo1981P2
/-!
# International Mathematical Olympiad 1981, Problem 2
Let $1 \le r \le n$ and consider all subsets of $r$ elements... | true | Copyright (c) 2026 Constantin Seebach. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Constantin Seebach
-/
import Mathlib
namespace Imo1981P2
/-!
# International Mathematical Olympiad 1981, Problem 2
Let $1 \le r \le n$ and consider all subsets of $r$ elements of... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo1981P2.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["unknown identifier 'min'_eq_iff'", "`grind` failed\ncase grind.1\nn r : \u2115\ns : Finset \u2115\nh : s \u2208 powersetCard (r + 1) (Icc 0 n)\nleft : #(eraseMin s) = r\nright : 0 \u2209 eraseMin s\nh_1 : eraseMin s \u2209 powersetCard r (Icc 1 n)\nh_2 : s... | false | true | false | 7.0621 |
compfiles_Imo1981P3 | compfiles | Copyright (c) 2020 Kevin Lacker. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Lacker
-/
import Mathlib
open Int Nat Set
namespace Imo1981P3
/-!
# International Mathematical Olympiad 1981, Problem 3
Determine the maximum value of `m ^ 2 + n ^ 2`, where `m`... | /- | /-
Copyright (c) 2020 Kevin Lacker. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Lacker
-/
import Mathlib
open Int Nat Set
namespace Imo1981P3
/-!
# International Mathematical Olympiad 1981, Problem 3
Determine the maximum value of `m ^ 2 + n ^ 2`, where ... | true | Copyright (c) 2020 Kevin Lacker. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Lacker
-/
import Mathlib
open Int Nat Set
namespace Imo1981P3
/-!
# International Mathematical Olympiad 1981, Problem 3
Determine the maximum value of `m ^ 2 + n ^ 2`, where `m`... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo1981P3.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["failed to synthesize\n Decidable (ProblemPredicate 1981 987 1597)\n\nAdditional diagnostic information may be available using the `set_option diagnostics true` command.", "no goals to be solved"], "timeout_s": 600.0, "latency_s": 6.8505, "verified_at": "2... | false | true | false | 6.8505 |
compfiles_Imo1981P4 | compfiles | Copyright (c) 2026 Constantin Seebach. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Constantin Seebach
-/
import Mathlib
namespace Imo1981P4
/-!
# International Mathematical Olympiad 1981, Problem 4
(a) For which values of $n>2$ is there a set of $n$ consecutive... | /- | /-
Copyright (c) 2026 Constantin Seebach. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Constantin Seebach
-/
import Mathlib
namespace Imo1981P4
/-!
# International Mathematical Olympiad 1981, Problem 4
(a) For which values of $n>2$ is there a set of $n$ consecut... | true | Copyright (c) 2026 Constantin Seebach. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Constantin Seebach
-/
import Mathlib
namespace Imo1981P4
/-!
# International Mathematical Olympiad 1981, Problem 4
(a) For which values of $n>2$ is there a set of $n$ consecutive... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo1981P4.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["unknown identifier 'lcm_dvd_prod'", "unsolved goals\nn k : \u2115\nh : last_divides_lcm_remaining n k\n\u22a2 k + n \u2223 (n - 1).factorial", "unknown tactic", "unsolved goals\nk : \u2115\nthis\u271d : k + 3 \u2223 2\nthis : k + 3 \u2264 2\n\u22a2 False",... | false | true | false | 0.3095 |
compfiles_Imo1981P6 | compfiles | Copyright (c) 2023 David Renshaw. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Renshaw
-/
import Mathlib
/-!
# International Mathematical Olympiad 1981, Problem 6
Suppose that f : ℕ × ℕ → ℕ satisfies
1) f (0, y) = y + 1
2) f (x + 1, 0) = f (x, 1),
3) f... | /- | /-
Copyright (c) 2023 David Renshaw. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Renshaw
-/
import Mathlib
/-!
# International Mathematical Olympiad 1981, Problem 6
Suppose that f : ℕ × ℕ → ℕ satisfies
1) f (0, y) = y + 1
2) f (x + 1, 0) = f (x, 1),
3... | true | Copyright (c) 2023 David Renshaw. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Renshaw
-/
import Mathlib
/-!
# International Mathematical Olympiad 1981, Problem 6
Suppose that f : ℕ × ℕ → ℕ satisfies
1) f (0, y) = y + 1
2) f (x + 1, 0) = f (x, 1),
3) f... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo1981P6.lean"} | {"v4.21.0": {"is_valid": true, "has_sorry": false, "errors": [], "timeout_s": 600.0, "latency_s": 0.3745, "verified_at": "2026-03-26T18:16:46.586193+00:00"}} | true | true | false | 0.3745 |
compfiles_Imo1982P1 | compfiles | Copyright (c) 2023 David Renshaw. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Renshaw
-/
import Mathlib
/-!
# International Mathematical Olympiad 1982, Problem 1
Let f be a function from positive integers to nonnegative integers such that
1) f(2) = 0
2)... | /- | /-
Copyright (c) 2023 David Renshaw. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Renshaw
-/
import Mathlib
/-!
# International Mathematical Olympiad 1982, Problem 1
Let f be a function from positive integers to nonnegative integers such that
1) f(2) = 0
... | true | Copyright (c) 2023 David Renshaw. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Renshaw
-/
import Mathlib
/-!
# International Mathematical Olympiad 1982, Problem 1
Let f be a function from positive integers to nonnegative integers such that
1) f(2) = 0
2)... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo1982P1.lean"} | {"v4.21.0": {"is_valid": true, "has_sorry": false, "errors": [], "timeout_s": 120, "latency_s": 1.7846, "verified_at": "2026-03-30T14:41:51.094513+00:00"}} | true | true | false | 1.7846 |
compfiles_Imo1982P3 | compfiles | Copyright (c) 2024 Violeta Hernández Palacios. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Violeta Hernández Palacios, Alex Brodbelt
-/
import Mathlib
/-!
# International Mathematical Olympiad 1982, Problem 3
Consider infinite sequences $\{x_n \}$ of positive re... | /- | /-
Copyright (c) 2024 Violeta Hernández Palacios. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Violeta Hernández Palacios, Alex Brodbelt
-/
import Mathlib
/-!
# International Mathematical Olympiad 1982, Problem 3
Consider infinite sequences $\{x_n \}$ of positive... | true | Copyright (c) 2024 Violeta Hernández Palacios. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Violeta Hernández Palacios, Alex Brodbelt
-/
import Mathlib
/-!
# International Mathematical Olympiad 1982, Problem 3
Consider infinite sequences $\{x_n \}$ of positive re... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo1982P3.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["unknown constant 'Finset.nonempty_range_add_one'"], "timeout_s": 600.0, "latency_s": 2.3867, "verified_at": "2026-03-26T18:16:55.073628+00:00"}} | false | true | false | 2.3867 |
compfiles_Imo1982P4 | compfiles | Copyright (c) 2024 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: InternLM-MATH LEAN Formalizer v0.1, Goedel-Prover-V2
-/
import Mathlib
/-!
# International Mathematical Olympiad 1982, Problem 4
Prove that if n is a positive integer suc... | /- | /-
Copyright (c) 2024 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: InternLM-MATH LEAN Formalizer v0.1, Goedel-Prover-V2
-/
import Mathlib
/-!
# International Mathematical Olympiad 1982, Problem 4
Prove that if n is a positive integer ... | true | Copyright (c) 2024 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: InternLM-MATH LEAN Formalizer v0.1, Goedel-Prover-V2
-/
import Mathlib
/-!
# International Mathematical Olympiad 1982, Problem 4
Prove that if n is a positive integer suc... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo1982P4.lean"} | {"v4.21.0": {"is_valid": true, "has_sorry": false, "errors": [], "timeout_s": 120, "latency_s": 6.682, "verified_at": "2026-03-30T14:41:55.245255+00:00"}} | true | true | false | 6.682 |
compfiles_Imo1983P1 | compfiles | Copyright (c) 2024 David Renshaw. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Renshaw
-/
import Mathlib
/-!
# International Mathematical Olympiad 1983, Problem 1
Let ℝ+ be the set of positive real numbers.
Determine all functions f : ℝ+ → ℝ+ which satisf... | /- | /-
Copyright (c) 2024 David Renshaw. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Renshaw
-/
import Mathlib
/-!
# International Mathematical Olympiad 1983, Problem 1
Let ℝ+ be the set of positive real numbers.
Determine all functions f : ℝ+ → ℝ+ which sat... | true | Copyright (c) 2024 David Renshaw. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Renshaw
-/
import Mathlib
/-!
# International Mathematical Olympiad 1983, Problem 1
Let ℝ+ be the set of positive real numbers.
Determine all functions f : ℝ+ → ℝ+ which satisf... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo1983P1.lean"} | {"v4.21.0": {"is_valid": true, "has_sorry": false, "errors": [], "timeout_s": 600.0, "latency_s": 6.3627, "verified_at": "2026-03-26T18:16:59.050015+00:00"}} | true | true | false | 6.3627 |
compfiles_Imo1983P5 | compfiles | Copyright (c) 2024 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: InternLM-MATH LEAN Formalizer v0.1, Benpigchu
-/
import Mathlib
/-!
# International Mathematical Olympiad 1983, Problem 5
Is it possible to choose $1983$ distinct positiv... | /- | /-
Copyright (c) 2024 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: InternLM-MATH LEAN Formalizer v0.1, Benpigchu
-/
import Mathlib
/-!
# International Mathematical Olympiad 1983, Problem 5
Is it possible to choose $1983$ distinct posi... | true | Copyright (c) 2024 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: InternLM-MATH LEAN Formalizer v0.1, Benpigchu
-/
import Mathlib
/-!
# International Mathematical Olympiad 1983, Problem 5
Is it possible to choose $1983$ distinct positiv... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo1983P5.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["unknown tactic", "unknown constant 'Nat.getD_digits'", "unsolved goals\nn i b : \u2115\nh : 2 \u2264 b\n\u22a2 ?m.3734 > 0", "unknown tactic", "unsolved goals\ncase h\nb : \u2115\nhb : 2 \u2264 b\nm : \u2115\nh' :\n \u2200 m_1 < m,\n \u2200 (n : \u2115... | false | true | false | 0.6645 |
compfiles_Imo1983P6 | compfiles | Copyright (c) 2024 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Roozbeh Yousefzadeh, David Renshaw
-/
import Mathlib
/-!
# International Mathematical Olympiad 1983, Problem 6
Suppose that a,b,c are the side lengths of a triangle. Prov... | /- | /-
Copyright (c) 2024 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Roozbeh Yousefzadeh, David Renshaw
-/
import Mathlib
/-!
# International Mathematical Olympiad 1983, Problem 6
Suppose that a,b,c are the side lengths of a triangle. P... | true | Copyright (c) 2024 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Roozbeh Yousefzadeh, David Renshaw
-/
import Mathlib
/-!
# International Mathematical Olympiad 1983, Problem 6
Suppose that a,b,c are the side lengths of a triangle. Prov... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo1983P6.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["type mismatch\n hr1\nhas type\n z * (y * z ^ 3) = x * (x * y ^ 3) : Prop\nbut is expected to have type\n z ^ 4 = x ^ 2 * y ^ 2 : Prop", "type mismatch\n hr2\nhas type\n z * (z * x ^ 3) = y * (x * y ^ 3) : Prop\nbut is expected to have type\n z ^ 2 * ... | false | true | false | 7.2555 |
compfiles_Imo1984P1 | compfiles | Copyright (c) 2024 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: InternLM-MATH LEAN Formalizer v0.1, Hongyu Ouyang
-/
import Mathlib
/-!
# International Mathematical Olympiad 1984, Problem 1
Let $x$, $y$, $z$ be nonnegative real number... | /- | /-
Copyright (c) 2024 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: InternLM-MATH LEAN Formalizer v0.1, Hongyu Ouyang
-/
import Mathlib
/-!
# International Mathematical Olympiad 1984, Problem 1
Let $x$, $y$, $z$ be nonnegative real num... | true | Copyright (c) 2024 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: InternLM-MATH LEAN Formalizer v0.1, Hongyu Ouyang
-/
import Mathlib
/-!
# International Mathematical Olympiad 1984, Problem 1
Let $x$, $y$, $z$ be nonnegative real number... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo1984P1.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["no goals to be solved"], "timeout_s": 600.0, "latency_s": 3.0178, "verified_at": "2026-03-26T18:16:57.415356+00:00"}} | false | true | false | 3.0178 |
compfiles_Imo1984P2 | compfiles | Copyright (c) 2024 David Renshaw. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Renshaw
-/
import Mathlib
/-!
# International Mathematical Olympiad 1984, Problem 2
Find a pair of positive integers a and b such that
(i) ab(a + b) is not divisible by 7.
(i... | /- | /-
Copyright (c) 2024 David Renshaw. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Renshaw
-/
import Mathlib
/-!
# International Mathematical Olympiad 1984, Problem 2
Find a pair of positive integers a and b such that
(i) ab(a + b) is not divisible by 7.
... | true | Copyright (c) 2024 David Renshaw. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Renshaw
-/
import Mathlib
/-!
# International Mathematical Olympiad 1984, Problem 2
Find a pair of positive integers a and b such that
(i) ab(a + b) is not divisible by 7.
(i... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo1984P2.lean"} | {"v4.21.0": {"is_valid": true, "has_sorry": false, "errors": [], "timeout_s": 600.0, "latency_s": 0.0625, "verified_at": "2026-03-26T18:16:55.136288+00:00"}} | true | true | false | 0.0625 |
compfiles_Imo1984P6 | compfiles | Copyright (c) 2025 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Roozbeh Yousefzadeh
-/
import Mathlib
/-!
# International Mathematical Olympiad 1984, Problem 6
Let a, b, c, and d be odd integers such that 0 < a < b < c < d and ad = bc... | /- | /-
Copyright (c) 2025 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Roozbeh Yousefzadeh
-/
import Mathlib
/-!
# International Mathematical Olympiad 1984, Problem 6
Let a, b, c, and d be odd integers such that 0 < a < b < c < d and ad =... | true | Copyright (c) 2025 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Roozbeh Yousefzadeh
-/
import Mathlib
/-!
# International Mathematical Olympiad 1984, Problem 6
Let a, b, c, and d be odd integers such that 0 < a < b < c < d and ad = bc... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo1984P6.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["unknown tactic", "unsolved goals\na b : \u2115\nh\u2080 : b < a\nh\u2081 : b ^ 2 \u2264 a * b\nh\u2082 : a * b \u2264 a ^ 2\n\u22a2 a ^ 2 - (a * b - b ^ 2) - a * b = a ^ 2 + b ^ 2 - a * b * 2", "unknown tactic", "unsolved goals\na b c d k m : \u2115\nh\u20... | false | true | false | 1.5153 |
compfiles_Imo1985P2 | compfiles | Copyright (c) 2025 Jeremy Tan. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Tan
-/
import Mathlib
/-!
# International Mathematical Olympiad 1985, Problem 2
Fix a natural number $n ≥ 3$ and define $N=\{1, 2, 3, \dots, n-1\}$.
Fix another natural number $j ∈... | /- | /-
Copyright (c) 2025 Jeremy Tan. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Tan
-/
import Mathlib
/-!
# International Mathematical Olympiad 1985, Problem 2
Fix a natural number $n ≥ 3$ and define $N=\{1, 2, 3, \dots, n-1\}$.
Fix another natural number $... | true | Copyright (c) 2025 Jeremy Tan. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Tan
-/
import Mathlib
/-!
# International Mathematical Olympiad 1985, Problem 2
Fix a natural number $n ≥ 3$ and define $N=\{1, 2, 3, \dots, n-1\}$.
Fix another natural number $j ∈... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo1985P2.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["unknown tactic", "tactic 'rewrite' failed, did not find instance of the pattern in the target expression\n (k + 1) % n\nn j : \u2115\nhn : 3 \u2264 n\nhj : j \u2208 Set.Ico 1 n\ncpj : n.Coprime j\nC : \u2115 \u2192 Fin 2\nhC : Condition n j C\nk\u271d k :... | false | true | false | 0.102 |
compfiles_Imo1985P4 | compfiles | Copyright (c) 2024 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Benpigchu
-/
import Mathlib
/-!
# International Mathematical Olympiad 1985, Problem 4
Given a set M of 1985 distinct positive integers, none of which has a prime
divisor ... | /- | /-
Copyright (c) 2024 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Benpigchu
-/
import Mathlib
/-!
# International Mathematical Olympiad 1985, Problem 4
Given a set M of 1985 distinct positive integers, none of which has a prime
divis... | true | Copyright (c) 2024 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Benpigchu
-/
import Mathlib
/-!
# International Mathematical Olympiad 1985, Problem 4
Given a set M of 1985 distinct positive integers, none of which has a prime
divisor ... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo1985P4.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["unknown tactic", "unsolved goals\n\u03b1 : Type u\n\u03b2 : Type v\ninst\u271d\u00b9 : DecidableEq \u03b1\ninst\u271d : DecidableEq \u03b2\ns : Finset \u03b1\nf : \u03b1 \u2192 \u03b2\ns' : Finset \u03b2\nhf : \u2200 n \u2208 s, f n \u2208 s'\nn' : \u2115\... | false | true | false | 0.9721 |
compfiles_Imo1985P6 | compfiles | Copyright (c) 2025 Roozbeh Yousefzadeh. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Roozbeh Yousefzadeh
-/
import Mathlib
/-!
# International Mathematical Olympiad 1985, Problem 6
For every real number x_1, construct the sequence {x_1,x_2, ...}
by setting x_{n+... | /- | /-
Copyright (c) 2025 Roozbeh Yousefzadeh. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Roozbeh Yousefzadeh
-/
import Mathlib
/-!
# International Mathematical Olympiad 1985, Problem 6
For every real number x_1, construct the sequence {x_1,x_2, ...}
by setting x_... | true | Copyright (c) 2025 Roozbeh Yousefzadeh. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Roozbeh Yousefzadeh
-/
import Mathlib
/-!
# International Mathematical Olympiad 1985, Problem 6
For every real number x_1, construct the sequence {x_1,x_2, ...}
by setting x_{n+... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo1985P6.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["unknown tactic", "unsolved goals\nf : \u2115 \u2192 NNReal \u2192 \u211d\nh\u2080 : \u2200 (x : NNReal), f 1 x = \u2191x\nh\u2081 : \u2200 (n : \u2115) (x : NNReal), 0 < n \u2192 f (n + 1) x = f n x * (f n x + 1 / \u2191n)\nh\u2084 : \u2200 (n : \u2115) (x... | false | true | false | 6.8817 |
compfiles_Imo1986P1 | compfiles | Copyright (c) 2023 Moritz Firsching. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Moritz Firsching
-/
import Mathlib
/-!
# International Mathematical Olympiad 1986, Problem 1
Let d be any positive integer not equal to 2, 5 or 13.
Show that one can find distinct a... | /- | /-
Copyright (c) 2023 Moritz Firsching. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Moritz Firsching
-/
import Mathlib
/-!
# International Mathematical Olympiad 1986, Problem 1
Let d be any positive integer not equal to 2, 5 or 13.
Show that one can find distinc... | true | Copyright (c) 2023 Moritz Firsching. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Moritz Firsching
-/
import Mathlib
/-!
# International Mathematical Olympiad 1986, Problem 1
Let d be any positive integer not equal to 2, 5 or 13.
Show that one can find distinct a... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo1986P1.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["`grind` failed\ncase grind.1.1.2.2.2.2.2.2\nd p : \u2124\nhp : 2 * d + -1 * p ^ 2 + -1 = 0\nq : \u2124\nhq : 5 * d + -1 * q ^ 2 + -1 = 0\nr : \u2124\nhr : 13 * d + -1 * r ^ 2 + -1 = 0\nk : \u2124\nhk : p = 2 * k + 1\nhp_1 : -2 * d + p ^ 2 + 1 = 0\nhdp : d ... | false | true | false | 1.654 |
compfiles_Imo1986P3 | compfiles | Copyright (c) 2026 lean-tom. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: lean-tom (with assistance from Gemini)
-/
import Mathlib
/-!
# International Mathematical Olympiad 1986, Problem 3
To each vertex of a regular pentagon, an integer is assigned,
in such a w... | /- | /-
Copyright (c) 2026 lean-tom. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: lean-tom (with assistance from Gemini)
-/
import Mathlib
/-!
# International Mathematical Olympiad 1986, Problem 3
To each vertex of a regular pentagon, an integer is assigned,
in such ... | true | Copyright (c) 2026 lean-tom. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: lean-tom (with assistance from Gemini)
-/
import Mathlib
/-!
# International Mathematical Olympiad 1986, Problem 3
To each vertex of a regular pentagon, an integer is assigned,
in such a w... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo1986P3.lean"} | {"v4.21.0": {"is_valid": true, "has_sorry": false, "errors": [], "timeout_s": 600.0, "latency_s": 2.6326, "verified_at": "2026-03-26T18:17:01.682720+00:00"}} | true | true | false | 2.6326 |
compfiles_Imo1986P5 | compfiles | Copyright (c) 2024 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Mathlib
/-!
# International Mathematical Olympiad 1986, Problem 5
Find all functions `f`, defined on the non-negative real numbers and taking nonnegative re... | /- | /-
Copyright (c) 2024 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Mathlib
/-!
# International Mathematical Olympiad 1986, Problem 5
Find all functions `f`, defined on the non-negative real numbers and taking nonnegative... | true | Copyright (c) 2024 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Mathlib
/-!
# International Mathematical Olympiad 1986, Problem 5
Find all functions `f`, defined on the non-negative real numbers and taking nonnegative re... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo1986P5.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["failed to synthesize\n LE Type\n\nAdditional diagnostic information may be available using the `set_option diagnostics true` command.", "failed to synthesize\n LE Type\n\nAdditional diagnostic information may be available using the `set_option diagnostic... | false | true | false | 1.1394 |
compfiles_Imo1987P1 | compfiles | Copyright (c) 2021 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Mathlib
/-!
# International Mathematical Olympiad 1987, Problem 1
Let $p_{n, k}$ be the number of permutations of a set of cardinality `n ≥ 1`
that fix exac... | /- | /-
Copyright (c) 2021 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Mathlib
/-!
# International Mathematical Olympiad 1987, Problem 1
Let $p_{n, k}$ be the number of permutations of a set of cardinality `n ≥ 1`
that fix e... | true | Copyright (c) 2021 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Mathlib
/-!
# International Mathematical Olympiad 1987, Problem 1
Let $p_{n, k}$ be the number of permutations of a set of cardinality `n ≥ 1`
that fix exac... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo1987P1.lean"} | {"v4.21.0": {"is_valid": true, "has_sorry": false, "errors": [], "timeout_s": 600.0, "latency_s": 11.917, "verified_at": "2026-03-26T18:17:12.437650+00:00"}} | true | true | false | 11.917 |
compfiles_Imo1987P4 | compfiles | Copyright (c) 2023 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Renshaw
-/
import Mathlib
/-!
# International Mathematical Olympiad 1987, Problem 4
Prove that there is no function f : ℕ → ℕ such that f(f(n)) = n + 1987
for every... | /- | /-
Copyright (c) 2023 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Renshaw
-/
import Mathlib
/-!
# International Mathematical Olympiad 1987, Problem 4
Prove that there is no function f : ℕ → ℕ such that f(f(n)) = n + 1987
for ev... | true | Copyright (c) 2023 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Renshaw
-/
import Mathlib
/-!
# International Mathematical Olympiad 1987, Problem 4
Prove that there is no function f : ℕ → ℕ such that f(f(n)) = n + 1987
for every... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo1987P4.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["unknown tactic", "unknown constant 'Set.ncard_coe_finset'", "unsolved goals\ncase intro.intro\nm : \u2115\nf : \u2115 \u2192 \u2115\nhf : \u2200 (n : \u2115), f (f n) = n + (2 * m + 1)\nf_injective : Function.Injective f\nA : Set \u2115 := Set.univ \\ f ''... | false | true | false | 0.1761 |
compfiles_Imo1987P6 | compfiles | Copyright (c) 2025 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jia-Jun Ma
-/
import Mathlib
/-!
# International Mathematical Olympiad 1987, Problem 6
Let $n$ be an integer greater than or equal to 2. Prove that
if $k^2 + k + n$ is pri... | /- | /-
Copyright (c) 2025 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jia-Jun Ma
-/
import Mathlib
/-!
# International Mathematical Olympiad 1987, Problem 6
Let $n$ be an integer greater than or equal to 2. Prove that
if $k^2 + k + n$ is ... | true | Copyright (c) 2025 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jia-Jun Ma
-/
import Mathlib
/-!
# International Mathematical Olympiad 1987, Problem 6
Let $n$ be an integer greater than or equal to 2. Prove that
if $k^2 + k + n$ is pri... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo1987P6.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["unknown tactic", "Missing cases:\n(succ _), _", "unsolved goals\nn\u271d n : \u2115\nhnezero : n + 2 \u2260 0\nhn : (n + 2).minFac \u2260 n + 2\nr : \u2115\nhr : n + 2 = (n + 2).minFac * 0\n\u22a2 (n + 2).minFac ^ 2 \u2264 n + 2", "unknown tactic", "unsolv... | false | true | false | 0.8114 |
compfiles_Imo1988P3 | compfiles | Copyright (c) 2024 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: InternLM-MATH LEAN Formalizer v0.1, Goedel-Prover-V2
-/
import Mathlib
/-!
# International Mathematical Olympiad 1988, Problem 3
A function $f$ defined on the positive in... | /- | /-
Copyright (c) 2024 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: InternLM-MATH LEAN Formalizer v0.1, Goedel-Prover-V2
-/
import Mathlib
/-!
# International Mathematical Olympiad 1988, Problem 3
A function $f$ defined on the positive... | false | null | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo1988P3.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": true, "errors": [], "timeout_s": 600.0, "latency_s": 0.0558, "verified_at": "2026-03-26T18:17:12.495340+00:00"}} | false | true | true | 0.0558 |
compfiles_Imo1988P6 | compfiles | Copyright (c) 2019 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
import Mathlib
/-!
# International Mathematical Olympiad 1988, Problem 6
If a and b are two natural numbers such that a*b+1 divides a^2 + b^2,
show that their quoti... | /- | /-
Copyright (c) 2019 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
import Mathlib
/-!
# International Mathematical Olympiad 1988, Problem 6
If a and b are two natural numbers such that a*b+1 divides a^2 + b^2,
show that their qu... | true | Copyright (c) 2019 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
import Mathlib
/-!
# International Mathematical Olympiad 1988, Problem 6
If a and b are two natural numbers such that a*b+1 divides a^2 + b^2,
show that their quoti... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo1988P6.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["unknown tactic", "Application type mismatch: In the application\n @WellFounded.not_lt_min \u2115 WellFoundedRelation.rel WellFoundedRelation.wf S hk\nthe argument\n hk\nhas type\n k \u2208 S : Prop\nbut is expected to have type\n S.Nonempty : Prop", "u... | false | true | false | 0.5408 |
compfiles_Imo1989P1 | compfiles | Copyright (c) 2025 Francesco Vercellesi· All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Francesco Vercellesi
-/
import Mathlib
/-!
# International Mathematical Olympiad 1989, Problem 1
Prove that the integers from 1 to 1989 can be partitioned in 117 sets
of 17 ele... | /- | /-
Copyright (c) 2025 Francesco Vercellesi· All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Francesco Vercellesi
-/
import Mathlib
/-!
# International Mathematical Olympiad 1989, Problem 1
Prove that the integers from 1 to 1989 can be partitioned in 117 sets
of 17 ... | true | Copyright (c) 2025 Francesco Vercellesi· All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Francesco Vercellesi
-/
import Mathlib
/-!
# International Mathematical Olympiad 1989, Problem 1
Prove that the integers from 1 to 1989 can be partitioned in 117 sets
of 17 ele... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo1989P1.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["unknown tactic", "unsolved goals\ncase pos\nj : \u2115\nhj : j < 17\ni : Fin n\nh\u271d\u00b9 : j < 14\nh\u271d : j % 2 = 0\n\u22a2 (j * 117 + \u2191i) / 117 = j\n\ncase neg\nj : \u2115\nhj : j < 17\ni : Fin n\nh\u271d\u00b9 : j < 14\nh\u271d : j % 2 = 1\n... | false | true | false | 3.5145 |
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