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_Imo1989P5 | 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 1989, Problem 5
Prove that for each positive integer n there exist n consecutive positive
integers, none of w... | /- | /-
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 1989, Problem 5
Prove that for each positive integer n there exist n consecutive positive
integers, none o... | 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 1989, Problem 5
Prove that for each positive integer n there exist n consecutive positive
integers, none of w... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo1989P5.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["unknown constant 'Nat.Coprime.mul_left'", "unknown tactic", "unsolved goals\nn : \u2115\nl : List \u2115\nhll : l.length = 2 * n\nhld : l.Nodup\nhl : \u2200 x \u2208 l, Nat.Prime x \u2227 n \u2264 x\nx : Fin n\n\u22a2 \u2191x < l.length", "unsolved goals\n... | false | true | false | 1.3657 |
compfiles_Imo1989P6 | 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 1989, Problem 6
A permutation $\{x_1, \ldots, x_{2n}\}$ of the set $\{1,2, \ldots, 2n\}$ where $n$ ... | /- | /-
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 1989, Problem 6
A permutation $\{x_1, \ldots, x_{2n}\}$ of the set $\{1,2, \ldots, 2n\}$ where $... | 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 1989, Problem 6
A permutation $\{x_1, \ldots, x_{2n}\}$ of the set $\{1,2, \ldots, 2n\}$ where $n$ ... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo1989P6.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["`grind` failed\ncase grind.1\nn : \u2115\nx : { x // x \u2208 Finset.Icc 1 (2 * n) } \u2243 { x // x \u2208 Finset.Icc 1 (2 * n) }\ni : \u2115\nh : i \u2208 Finset.Icc 1 (2 * n - 1)\nh_1 : i \u2209 Finset.Icc 1 (2 * n)\nh_2 : -1 * \u2191n + 1 \u2264 0\n\u2... | false | true | false | 6.4954 |
compfiles_Imo1990P3 | compfiles | Copyright (c) 2023 David Renshaw. 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 1990, Problem 3
Find all integers n > 1 such that n² divides 2ⁿ + 1.
-/
namespace Imo19... | /- | /-
Copyright (c) 2023 David Renshaw. 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 1990, Problem 3
Find all integers n > 1 such that n² divides 2ⁿ + 1.
-/
namespace Im... | true | Copyright (c) 2023 David Renshaw. 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 1990, Problem 3
Find all integers n > 1 such that n² divides 2ⁿ + 1.
-/
namespace Imo19... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo1990P3.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["unsolved goals\ncase \u00ab2\u00bb.h.h.zero\nn r : \u2115\nh\u2080 : 2 < 3\n\u22a2 4 \u2261 4 [MOD 7]", "unknown tactic", "unsolved goals\nn : \u2115\nh\u2080 : 2 \u2264 n\nh\u2081 : n ^ 2 \u2223 2 ^ n + 1\nhn\u2080 : 3 \u2264 n\nhc : Even n\n\u22a2 n \u22... | false | true | false | 0.2465 |
compfiles_Imo1990P4 | 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 1990, Problem 4
Let $\mathbb{Q^+}$ be the set of positive rational numbers.
Construct a function $f... | /- | /-
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 1990, Problem 4
Let $\mathbb{Q^+}$ be the set of positive rational numbers.
Construct a function... | 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 1990, Problem 4
Let $\mathbb{Q^+}$ be the set of positive rational numbers.
Construct a function $f... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo1990P4.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["unknown constant 'Rat.le_of_lt'", "unknown tactic", "invalid argument name 'motive' for function 'induction_on_primes'", "no goals to be solved", "unsolved goals\nP : \u211a+ \u2192 Prop\nbase : P 1\nind_mul : \u2200 (x : \u211a+) (p : Nat.Primes), P x \u2... | false | true | false | 5.0029 |
compfiles_Imo1991P2 | compfiles | Copyright (c) 2025 The Compfiles Authors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Benpigchu
-/
import Mathlib
/-!
# International Mathematical Olympiad 1991, Problem 2
Let n > 6 be an integer and a₁, a₂, ..., aₖ be all the
natural numbers less than n and re... | /- | /-
Copyright (c) 2025 The Compfiles Authors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Benpigchu
-/
import Mathlib
/-!
# International Mathematical Olympiad 1991, Problem 2
Let n > 6 be an integer and a₁, a₂, ..., aₖ be all the
natural numbers less than n and... | true | Copyright (c) 2025 The Compfiles Authors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Benpigchu
-/
import Mathlib
/-!
# International Mathematical Olympiad 1991, Problem 2
Let n > 6 be an integer and a₁, a₂, ..., aₖ be all the
natural numbers less than n and re... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo1991P2.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["unknown tactic", "unsolved goals\ncase hz\nhn : 0 < 0\n\u22a2 \u2203 t l, 0 = 2 ^ t * l \u2227 \u00ac2 \u2223 l", "unsolved goals\ncase hi\nn' : \u2115\nhn' : \u2200 m \u2264 n', 0 < m \u2192 \u2203 t l, m = 2 ^ t * l \u2227 \u00ac2 \u2223 l\nhn : 0 < n' +... | false | true | false | 0.2449 |
compfiles_Imo1991P5 | compfiles | Copyright (c) 2025 The Compfiles Authors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Benpigchu
-/
import Mathlib
/-!
# International Mathematical Olympiad 1991, Problem 5
Let ABC be a triangle and P be an interior point of ABC.
Show that at least one of the an... | /- | /-
Copyright (c) 2025 The Compfiles Authors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Benpigchu
-/
import Mathlib
/-!
# International Mathematical Olympiad 1991, Problem 5
Let ABC be a triangle and P be an interior point of ABC.
Show that at least one of the... | true | Copyright (c) 2025 The Compfiles Authors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Benpigchu
-/
import Mathlib
/-!
# International Mathematical Olympiad 1991, Problem 5
Let ABC be a triangle and P be an interior point of ABC.
Show that at least one of the an... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo1991P5.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["unknown tactic", "unsolved goals\na : \u211d\nha : \u03c0 / 6 < a\nha' : a < 5 * \u03c0 / 6\n\u22a2 Real.sin (\u03c0 / 6) < Real.sin a", "unknown tactic", "unsolved goals\nA B C P : EuclideanSpace \u211d (Fin 2)\nhABC : AffineIndependent \u211d ![A, B, C]\... | false | true | false | 6.9056 |
compfiles_Imo1991P6 | compfiles | Copyright (c) 2024 David Renshaw. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Renshaw, Constantin Seebach
-/
import Mathlib
/-!
# International Mathematical Olympiad 1991, Problem 6
An infinite sequence x₀,x₁,x₂,... of real numbers is said to be *bounded*... | /- | /-
Copyright (c) 2024 David Renshaw. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Renshaw, Constantin Seebach
-/
import Mathlib
/-!
# International Mathematical Olympiad 1991, Problem 6
An infinite sequence x₀,x₁,x₂,... of real numbers is said to be *bound... | true | Copyright (c) 2024 David Renshaw. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Renshaw, Constantin Seebach
-/
import Mathlib
/-!
# International Mathematical Olympiad 1991, Problem 6
An infinite sequence x₀,x₁,x₂,... of real numbers is said to be *bounded*... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo1991P6.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["Application type mismatch: In the application\n LT.lt.trans_eq (add_lt_add_left (sub_neg_of_lt h1) 1) (zero_add 1)\nthe argument\n zero_add 1\nhas type\n 0 + 1 = 1 : Prop\nbut is expected to have type\n 1 + 0 = ?m.74812 : Prop", "unknown tactic", "unso... | false | true | false | 5.0186 |
compfiles_Imo1992P1 | 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 1992, Problem 1
Find all integers 1 < a < b < c such that
(a - 1)(b - 1)(c - 1) divides ab... | /- | /-
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 1992, Problem 1
Find all integers 1 < a < b < c such that
(a - 1)(b - 1)(c - 1) divides... | 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 1992, Problem 1
Find all integers 1 < a < b < c such that
(a - 1)(b - 1)(c - 1) divides ab... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo1992P1.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["unknown tactic", "no goals to be solved", "unsolved goals\np q r : \u2124\nhpl : 4 \u2264 p\nhql : 5 \u2264 q\nhrl : 6 \u2264 r\nh\u2081 : \u2191(p * q * r) / \u2191((p - 1) * (q - 1) * (r - 1)) = \u2191p / \u2191(p - 1) * (\u2191q / \u2191(q - 1)) * (\u21... | false | true | false | 8.9352 |
compfiles_Imo1992P2 | 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 1992, Problem 2
Determine all functions f : ℝ → ℝ such that
for all x,y ∈ ℝ, f(x² + f(y)) = y + (f(x))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 1992, Problem 2
Determine all functions f : ℝ → ℝ such that
for all x,y ∈ ℝ, f(x² + f(y)) = y + (f(x))².
-... | 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 1992, Problem 2
Determine all functions f : ℝ → ℝ such that
for all x,y ∈ ℝ, f(x² + f(y)) = y + (f(x))².
-/
... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo1992P2.lean"} | {"v4.21.0": {"is_valid": true, "has_sorry": false, "errors": [], "timeout_s": 600.0, "latency_s": 1.0747, "verified_at": "2026-03-26T18:17:20.554117+00:00"}} | true | true | false | 1.0747 |
compfiles_Imo1992P5 | compfiles | Copyright (c) 2026 Sebastian Willmann. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sebastian Willmann (with assistance from Github Copilot and Aristotle)
-/
import Mathlib
/-!
# International Mathematical Olympiad 1992, Problem 5
Let S be a finite set of points... | /- | /-
Copyright (c) 2026 Sebastian Willmann. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sebastian Willmann (with assistance from Github Copilot and Aristotle)
-/
import Mathlib
/-!
# International Mathematical Olympiad 1992, Problem 5
Let S be a finite set of poi... | true | Copyright (c) 2026 Sebastian Willmann. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sebastian Willmann (with assistance from Github Copilot and Aristotle)
-/
import Mathlib
/-!
# International Mathematical Olympiad 1992, Problem 5
Let S be a finite set of points... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo1992P5.lean"} | {"v4.21.0": {"is_valid": true, "has_sorry": false, "errors": [], "timeout_s": 600.0, "latency_s": 1.1988, "verified_at": "2026-03-26T18:17:21.753019+00:00"}} | true | true | false | 1.1988 |
compfiles_Imo1992P6 | 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 1992, Problem 6
For each positive integer $n$, $S(n)$ is defined to be the greatest integer such th... | /- | /-
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 1992, Problem 6
For each positive integer $n$, $S(n)$ is defined to be the greatest integer such... | 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 1992, Problem 6
For each positive integer $n$, $S(n)$ is defined to be the greatest integer such th... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo1992P6.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["unsolved goals\ncase this\nn : \u2115+\ny : \u2115\nypos : 0 < y\nh : \u27e8y, \u22ef\u27e9 \u2208 S_set n\n\u22a2 ?m.14831\n\ncase h\nn : \u2115+\ny : \u2115\nypos : 0 < y\nh : \u27e8y, \u22ef\u27e9 \u2208 S_set n\nthis : ?m.14831 := ?this\n\u22a2 y \u226... | false | true | false | 12.3365 |
compfiles_Imo1993P1 | 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 1993, Problem 1
Let $f\left(x\right)=x^n+5x^{n-1}+3$, where $n>1$ is an integer.
Prove that $f\left... | /- | /-
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 1993, Problem 1
Let $f\left(x\right)=x^n+5x^{n-1}+3$, where $n>1$ is an integer.
Prove that $f\l... | 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 1993, Problem 1
Let $f\left(x\right)=x^n+5x^{n-1}+3$, where $n>1$ is an integer.
Prove that $f\left... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo1993P1.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["unknown tactic", "failed to synthesize\n Decidable (Prime (b.coeff 0) \u2227 IsUnit (c.coeff 0))\n\nAdditional diagnostic information may be available using the `set_option diagnostics true` command.", "no goals to be solved", "`grind` failed\ncase grind.... | false | true | false | 2.2868 |
compfiles_Imo1993P5 | 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, Zheng Yuan
-/
import Mathlib
/-!
# International Mathematical Olympiad 1993, Problem 5
Does there exist a function f : ℕ → ℕ such that
i) f(1) = 2
... | /- | /-
Copyright (c) 2024 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Roozbeh Yousefzadeh, Zheng Yuan
-/
import Mathlib
/-!
# International Mathematical Olympiad 1993, Problem 5
Does there exist a function f : ℕ → ℕ such that
i) f(1) =... | 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, Zheng Yuan
-/
import Mathlib
/-!
# International Mathematical Olympiad 1993, Problem 5
Does there exist a function f : ℕ → ℕ such that
i) f(1) = 2
... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo1993P5.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["unknown constant 'Real.goldenRatio'", "unknown constant 'Real.goldenRatio'", "unknown constant 'Real.goldenRatio_sq'", "failed to prove positivity/nonnegativity/nonzeroness", "linarith failed to find a contradiction\ncase h\nG : \u211d := sorry\nhG : G = s... | false | true | false | 4.4366 |
compfiles_Imo1994P1 | compfiles | Copyright (c) 2021 Antoine Labelle. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Antoine Labelle
-/
import Mathlib
/-!
# International Mathmatical Olympiad 1994, Problem 1
Let `m` and `n` be two positive integers.
Let `a₁, a₂, ..., aₘ` be `m` different numbers fr... | /- | /-
Copyright (c) 2021 Antoine Labelle. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Antoine Labelle
-/
import Mathlib
/-!
# International Mathmatical Olympiad 1994, Problem 1
Let `m` and `n` be two positive integers.
Let `a₁, a₂, ..., aₘ` be `m` different numbers... | true | Copyright (c) 2021 Antoine Labelle. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Antoine Labelle
-/
import Mathlib
/-!
# International Mathmatical Olympiad 1994, Problem 1
Let `m` and `n` be two positive integers.
Let `a₁, a₂, ..., aₘ` be `m` different numbers fr... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo1994P1.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["unknown tactic", "unsolved goals\nk c : \u2115\nhk : k < k + c + 1\n\u22a2 k + c + 1 - k + (k + c) = c + (k + c + 1)", "unsolved goals\ncase mk.intro\nk c : \u2115\nhk : k < k + c + 1\nthis : k + c + 1 - k + (k + c) = c + (k + c + 1)\n\u22a2 k + c - (k + c... | false | true | false | 0.1059 |
compfiles_Imo1994P4 | 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 1994, Problem 4
Determine all ordered pairs of positive integers (m, n) such that
(n³ +... | /- | /-
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 1994, Problem 4
Determine all ordered pairs of positive integers (m, n) such that
(n... | 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 1994, Problem 4
Determine all ordered pairs of positive integers (m, n) such that
(n³ +... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo1994P4.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["unknown tactic", "unsolved goals\na b : \u2124\nha : 0 \u2264 a\nhb : 0 \u2264 b\nhab : a * b = 2\n\u22a2 0 < a", "unsolved goals\na b : \u2124\nha : 0 \u2264 a\nhb : 0 \u2264 b\nhab : a * b = 2\nha_pos : 0 < a\n\u22a2 a = 1 \u2227 b = 2 \u2228 a = 2 \u222... | false | true | false | 0.9122 |
compfiles_Imo1994P5 | 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 1994, Problem 5
Let S be the set of all real numbers greater... | /- | /-
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 1994, Problem 5
Let S be the set of all real numbers grea... | 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 1994, Problem 5
Let S be the set of all real numbers greater... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo1994P5.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["`grind` failed\ncase grind\nf : S \u2192 S\nhf : f = fun x => \u27e8-\u2191x / (1 + \u2191x), \u22ef\u27e9\nx : \u211d\nhx : -1 < x\ny : \u211d\nhy : -1 < y\nh :\n \u00ac\u27e8-(x + -y / (1 + y) + x * (-y / (1 + y))) / (1 + (x + -y / (1 + y) + x * (-y / (... | false | true | false | 2.3622 |
compfiles_Imo1994P6 | compfiles | Copyright (c) 2026 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 1994, Problem 6
Show that there exists a set A of positive integers with the following
property: For an... | /- | /-
Copyright (c) 2026 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 1994, Problem 6
Show that there exists a set A of positive integers with the following
property: For... | true | Copyright (c) 2026 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 1994, Problem 6
Show that there exists a set A of positive integers with the following
property: For an... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo1994P6.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["`grind` failed\ncase grind\nk i : \u2115\nS : Set \u2115\nf : (fun x1 x2 => x1 \u2264 x2) \u2243r fun x1 x2 => x1 \u2264 x2\nhinj : Function.Injective fun j => f (i + j)\nh : \u00ac(Finset.range k).card = k\n\u22a2 False\n[grind] Goal diagnostics\n [facts... | false | true | false | 1.4464 |
compfiles_Imo1995P2 | compfiles | Copyright (c) 2024 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Zheng Yuan
-/
import Mathlib
/-!
# International Mathematical Olympiad 1995, Problem 2
Let a, b, c be positive real numbers such that abc = 1. Show that
1 / (a³(b + ... | /- | /-
Copyright (c) 2024 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Zheng Yuan
-/
import Mathlib
/-!
# International Mathematical Olympiad 1995, Problem 2
Let a, b, c be positive real numbers such that abc = 1. Show that
1 / (a³(b... | true | Copyright (c) 2024 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Zheng Yuan
-/
import Mathlib
/-!
# International Mathematical Olympiad 1995, Problem 2
Let a, b, c be positive real numbers such that abc = 1. Show that
1 / (a³(b + ... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo1995P2.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["tactic 'rewrite' failed, did not find instance of the pattern in the target expression\n \u221a(?m.158828 * ?y)\na b c : \u211d\nha : 0 < a\nhb : 0 < b\nhc : 0 < c\nhabc : a * b * c = 1\nf : Fin 3 \u2192 \u211d :=\n fun i =>\n match i with\n | 0 =>... | false | true | false | 6.7528 |
compfiles_Imo1995P4 | 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 1995, Problem 4
The positive real numbers $x_0, x_1, x_2,.....x_... | /- | /-
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 1995, Problem 4
The positive real numbers $x_0, x_1, x_2,....... | 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 1995, Problem 4
The positive real numbers $x_0, x_1, x_2,.....x_... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo1995P4.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["`grind` failed\ncase grind.1\na b : \u211d\nha : 0 < a\nhb : 0 < b\nh : (a + 2 / a = 2 * b + 1 / b) = (\u00acb = 1 / a \u2227 \u00acb = a / 2)\nleft : a + 2 / a = 2 * b + 1 / b\nleft_1 : \u00acb = 1 / a\nright_1 : \u00acb = a / 2\n\u22a2 False\n[grind] Goa... | false | true | false | 1.1151 |
compfiles_Imo1996P3 | 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 1996, Problem 3
Let S denote the set of nonnegative integers. Find
all functions f from S to its... | /- | /-
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 1996, Problem 3
Let S denote the set of nonnegative integers. Find
all functions f from S to ... | 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 1996, Problem 3
Let S denote the set of nonnegative integers. Find
all functions f from S to its... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo1996P3.lean"} | {"v4.21.0": {"is_valid": true, "has_sorry": false, "errors": [], "timeout_s": 120, "latency_s": 1.2974, "verified_at": "2026-03-30T14:45:02.834162+00:00"}} | true | true | false | 1.2974 |
compfiles_Imo1996P4 | compfiles | Copyright (c) 2025 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Rydh
-/
import Mathlib
/-!
# International Mathematical Olympiad 1996, Problem 4
The positive integers a and b are such that the numbers 15a + 16b
and 16a − 15b ar... | /- | /-
Copyright (c) 2025 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Rydh
-/
import Mathlib
/-!
# International Mathematical Olympiad 1996, Problem 4
The positive integers a and b are such that the numbers 15a + 16b
and 16a − 15b... | true | Copyright (c) 2025 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Rydh
-/
import Mathlib
/-!
# International Mathematical Olympiad 1996, Problem 4
The positive integers a and b are such that the numbers 15a + 16b
and 16a − 15b ar... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo1996P4.lean"} | {"v4.21.0": {"is_valid": true, "has_sorry": false, "errors": [], "timeout_s": 600.0, "latency_s": 5.2952, "verified_at": "2026-03-26T18:17:41.276714+00:00"}} | true | true | false | 5.2952 |
compfiles_Imo1996P6 | 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 1996, Problem 6
Let p, q, n be three positive integers with p + q < n. Let (x₀, x₁, . . . , xₙ)
be an ... | /- | /-
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 1996, Problem 6
Let p, q, n be three positive integers with p + q < n. Let (x₀, x₁, . . . , xₙ)
be ... | 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 1996, Problem 6
Let p, q, n be three positive integers with p + q < n. Let (x₀, x₁, . . . , xₙ)
be an ... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo1996P6.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["`grind` failed\ncase grind.2\np q : \u2124\nh\u2081 : \u00acp.sign = q.sign\nh\u2082 : \u00acp = 0\nh\u2083 : \u00acq = 0\nh : |p + -1 * q| + -1 \u2264 0\nh_1 : \u00acp = q\n\u22a2 False\n[grind] Goal diagnostics\n [facts] Asserted facts\n [prop] \u00a... | false | true | false | 5.6453 |
compfiles_Imo1997P3 | compfiles | Copyright (c) 2025 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Tan
-/
import Mathlib
/-!
# International Mathematical Olympiad 1997, Problem 3
Let $x_1, x_2, \dots, x_n$ be real numbers satisfying the conditions
$|x_1 + x_2 + ... | /- | /-
Copyright (c) 2025 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Tan
-/
import Mathlib
/-!
# International Mathematical Olympiad 1997, Problem 3
Let $x_1, x_2, \dots, x_n$ be real numbers satisfying the conditions
$|x_1 + x_2... | true | Copyright (c) 2025 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Tan
-/
import Mathlib
/-!
# International Mathematical Olympiad 1997, Problem 3
Let $x_1, x_2, \dots, x_n$ be real numbers satisfying the conditions
$|x_1 + x_2 + ... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo1997P3.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["Invalid alternative name 'one': Expected 'H1' or 'Hmul'", "unknown tactic", "unsolved goals\ncase a.h.e'_5\nn : \u2115\nx : Fin n \u2192 \u211d\nhx\u2081 : |\u2211 i, x i| = 1\ni : Fin n\na\u271d : i \u2208 Finset.univ\n\u22a2 \u2191i + 1 + (n - (\u2191i +... | false | true | false | 6.0205 |
compfiles_Imo1997P5 | 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, Ilmārs Cīrulis
-/
import Mathlib
/-!
# International Mathematical Olympiad 1997, Problem 5
Determine all pairs of integers 1 ≤ a,b that satisfy a ^ (... | /- | /-
Copyright (c) 2023 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Roozbeh Yousefzadeh, Ilmārs Cīrulis
-/
import Mathlib
/-!
# International Mathematical Olympiad 1997, Problem 5
Determine all pairs of integers 1 ≤ a,b that satisfy a ... | 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, Ilmārs Cīrulis
-/
import Mathlib
/-!
# International Mathematical Olympiad 1997, Problem 5
Determine all pairs of integers 1 ≤ a,b that satisfy a ^ (... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo1997P5.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["unknown tactic", "unsolved goals\nn\u271d b : \u2115\nhb : 2 \u2264 b\nn : \u2115\nhn : 5 \u2264 n\niH : n < b ^ (n - 2)\n\u22a2 n + 1 - 2 = n - 2 + 1", "unsolved goals\ncase succ\nn\u271d b : \u2115\nhb : 2 \u2264 b\nn : \u2115\nhn : 5 \u2264 n\niH : n < ... | false | true | false | 1.1963 |
compfiles_Imo1998P2 | compfiles | Copyright (c) 2020 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash
-/
import Mathlib
/-!
# International Mathematical Olympiad 1998, Problem 2
In a competition, there are `a` contestants and `b` judges, where `b ≥ 3` is
an odd integer. Each ... | /- | /-
Copyright (c) 2020 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash
-/
import Mathlib
/-!
# International Mathematical Olympiad 1998, Problem 2
In a competition, there are `a` contestants and `b` judges, where `b ≥ 3` is
an odd integer. Ea... | true | Copyright (c) 2020 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash
-/
import Mathlib
/-!
# International Mathematical Olympiad 1998, Problem 2
In a competition, there are `a` contestants and `b` judges, where `b ≥ 3` is
an odd integer. Each ... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo1998P2.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["failed to synthesize\n DecidablePred fun c => JudgePair.Agree r p c\n\nAdditional diagnostic information may be available using the `set_option diagnostics true` command.", "failed to synthesize\n DecidablePred fun a => JudgePair.Agree r a.judgePair a.co... | false | true | false | 1.8736 |
compfiles_Imo1998P3 | compfiles | Copyright (c) 2024 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: John Rathgeber
-/
import Mathlib
/-!
# International Mathematical Olympiad 1998, Problem 3
For any positive integer $n$,
let $d(n)$ denote the number of positive divisors... | /- | /-
Copyright (c) 2024 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: John Rathgeber
-/
import Mathlib
/-!
# International Mathematical Olympiad 1998, Problem 3
For any positive integer $n$,
let $d(n)$ denote the number of positive divis... | true | Copyright (c) 2024 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: John Rathgeber
-/
import Mathlib
/-!
# International Mathematical Olympiad 1998, Problem 3
For any positive integer $n$,
let $d(n)$ denote the number of positive divisors... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo1998P3.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["invalid field 'max', the environment does not contain 'List.max'\n existing_numbers\nhas type\n List \u2115", "unknown constant 'List.nodup_iff_pairwise_ne'", "unknown tactic", "unsolved goals\ncase h\nk_minus_1 : \u2115\nih : \u2200 m < k_minus_1 + 1, m... | false | true | false | 1.059 |
compfiles_Imo1998P4 | 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 1998, Problem 4
Determine all pairs (a, b) 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: InternLM-MATH LEAN Formalizer v0.1, Benpigchu
-/
import Mathlib
/-!
# International Mathematical Olympiad 1998, Problem 4
Determine all pairs (a, b) 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: InternLM-MATH LEAN Formalizer v0.1, Benpigchu
-/
import Mathlib
/-!
# International Mathematical Olympiad 1998, Problem 4
Determine all pairs (a, b) of positive integers ... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo1998P4.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["unknown tactic", "unsolved goals\ncase h.left\na b : \u2124\nha : 0 < a\nhb : 0 < b\nh : a * b ^ 2 + b + 7 \u2223 a ^ 2 * b + a + b\nh' : 7 + a * b ^ 2 + b \u2223 -(a * 7) + b ^ 2\nhab : -(a * 7) + b ^ 2 = 0\nk : \u2124\nhk : b = k * 7\n\u22a2 0 < k", "uns... | false | true | false | 0.2758 |
compfiles_Imo1998P6 | 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
-/
import Mathlib
/-!
# International Mathematical Olympiad 1998, Problem 6
Consider all functions f from the set of all positive integ... | /- | /-
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
-/
import Mathlib
/-!
# International Mathematical Olympiad 1998, Problem 6
Consider all functions f from the set of all positive in... | false | null | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo1998P6.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": true, "errors": [], "timeout_s": 600.0, "latency_s": 0.0487, "verified_at": "2026-03-26T18:17:42.500319+00:00"}} | false | true | true | 0.0487 |
compfiles_Imo1999P3 | 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 1999, Problem 3
Consider an `n × n` square board, where `n` is a fixed even positive intege... | /- | /-
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 1999, Problem 3
Consider an `n × n` square board, where `n` is a fixed even positive int... | 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 1999, Problem 3
Consider an `n × n` square board, where `n` is a fixed even positive intege... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo1999P3.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["unknown identifier 'mem_filter_univ'", "unknown identifier 'mem_filter_univ'"], "timeout_s": 600.0, "latency_s": 44.6683, "verified_at": "2026-03-26T18:18:28.440432+00:00"}} | false | true | false | 44.6683 |
compfiles_Imo1999P4 | 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 1999, Problem 4
Determine all pairs of positive integers (n,p) such that p is
a prime, n not exceede... | /- | /-
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 1999, Problem 4
Determine all pairs of positive integers (n,p) such that p is
a prime, n not exce... | 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 1999, Problem 4
Determine all pairs of positive integers (n,p) such that p is
a prime, n not exceede... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo1999P4.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["unknown constant 'ZMod.natCast_eq_zero_iff'", "Application type mismatch: In the application\n eq_neg_of_add_eq_zero_left hpa\nthe argument\n hpa\nhas type\n p \u2223 a ^ n + 1 : Prop\nbut is expected to have type\n \u2191a ^ n + 1 = 0 : Prop", "tactic... | false | true | false | 13.3722 |
compfiles_Imo1999P6 | 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 1999, Problem 6
Determine all functions f : ℝ → ℝ such that
f(x - f(y)) = f(f(y)) + xf(y) + f(x) - 1
for ... | /- | /-
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 1999, Problem 6
Determine all functions f : ℝ → ℝ such that
f(x - f(y)) = f(f(y)) + xf(y) + f(x) - 1
f... | 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 1999, Problem 6
Determine all functions f : ℝ → ℝ such that
f(x - f(y)) = f(f(y)) + xf(y) + f(x) - 1
for ... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo1999P6.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["no goals to be solved", "`grind` failed\ncase grind\nf : \u211d \u2192 \u211d\nhf : \u2200 (x y : \u211d), f (x - f y) = f (f y) + x * f y + f x - 1\nh1 : \u2200 a \u2208 Set.range f, f a = (1 + f 0) / 2 - a ^ 2 / 2\nh2 : \u2200 (x : \u211d), \u2203 a \u22... | false | true | false | 1.3101 |
compfiles_Imo2000P2 | 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 2000, Problem 2
Let a, b, c be positive real numbers such that abc = 1. Show that
(a - 1 + 1/b)(b - 1 + ... | /- | /-
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 2000, Problem 2
Let a, b, c be positive real numbers such that abc = 1. Show that
(a - 1 + 1/b)(b - 1... | 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 2000, Problem 2
Let a, b, c be positive real numbers such that abc = 1. Show that
(a - 1 + 1/b)(b - 1 + ... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo2000P2.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["`grind` failed\ncase grind\nx y z : \u211d\nhx : 0 < x\nhy : 0 < y\nhz : 0 < z\nha : 0 < x / y\nhb : 0 < y / z\nhc : 0 < z / x\nhabc : x / y * (y / z) * (z / x) = 1\nh1 : (-x + y + z) * (x - y + z) * (x + y - z) \u2264 x * y * z\nh2 : 0 < y * z * x\nH : (x... | false | true | false | 2.1239 |
compfiles_Imo2000P5 | compfiles | Copyright (c) 2025 The Compfiles Authors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors:
-/
import Mathlib
/-!
# International Mathematical Olympiad 2000, Problem 5
Does there exist a positive integer n such that n has exactly
2000 distinct prime divisors and n di... | /- | /-
Copyright (c) 2025 The Compfiles Authors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors:
-/
import Mathlib
/-!
# International Mathematical Olympiad 2000, Problem 5
Does there exist a positive integer n such that n has exactly
2000 distinct prime divisors and n... | false | null | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo2000P5.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": true, "errors": [], "timeout_s": 600.0, "latency_s": 0.0364, "verified_at": "2026-03-26T18:17:45.119385+00:00"}} | false | true | true | 0.0364 |
compfiles_Imo2001P1 | 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 2001, Problem 1
Let ABC be an acute-angled triangle with O as its circumcenter. Let P
on line BC b... | /- | /-
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 2001, Problem 1
Let ABC be an acute-angled triangle with O as its circumcenter. Let P
on line B... | 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 2001, Problem 1
Let ABC be an acute-angled triangle with O as its circumcenter. Let P
on line BC b... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo2001P1.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["unknown constant 'Module.Basis.orientation'", "type mismatch\n add_le_add_left hx' y\nhas type\n y + 0 \u2264 y + x : Prop\nbut is expected to have type\n 0 + y \u2264 x + y : Prop", "type mismatch\n add_le_add_right hy' x\nhas type\n y + x \u2264 0 +... | false | true | false | 9.2182 |
compfiles_Imo2001P2 | 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 2001, Problem 2
Let a, b, c be positive reals. Prove that
a / √(a² + 8bc) + b / √(b² + 8ca) + c / √(c² + 8ab) ≥ 1... | /- | /-
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 2001, Problem 2
Let a, b, c be positive reals. Prove that
a / √(a² + 8bc) + b / √(b² + 8ca) + c / √(c² + 8ab) ... | 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 2001, Problem 2
Let a, b, c be positive reals. Prove that
a / √(a² + 8bc) + b / √(b² + 8ca) + c / √(c² + 8ab) ≥ 1... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo2001P2.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["function expected at\n sqrt\nterm has type\n ?m.281", "failed to prove positivity/nonnegativity/nonzeroness", "function expected at\n sqrt\nterm has type\n x\u271d", "function expected at\n sqrt\nterm has type\n x\u271d", "unknown identifier 'sq_sqrt... | false | true | false | 0.8919 |
compfiles_Imo2001P3 | compfiles | Copyright (c) 2024 the Compfiles Contributers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Tan, David Renshaw
-/
import Mathlib
/-!
# International Mathematical Olympiad 2001, Problem 3
Twenty-one girls and twenty-one boys took part in a mathematical com... | /- | /-
Copyright (c) 2024 the Compfiles Contributers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Tan, David Renshaw
-/
import Mathlib
/-!
# International Mathematical Olympiad 2001, Problem 3
Twenty-one girls and twenty-one boys took part in a mathematical ... | true | Copyright (c) 2024 the Compfiles Contributers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Tan, David Renshaw
-/
import Mathlib
/-!
# International Mathematical Olympiad 2001, Problem 3
Twenty-one girls and twenty-one boys took part in a mathematical com... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo2001P3.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["unknown tactic", "unsolved goals\n\u03b1 \u03b2 : Type\ninst\u271d : Fintype \u03b1\n\u03b2_solved : \u03b2 \u2192 Finset \u2115\n\u03b1_solved : \u03b1 \u2192 Finset \u2115\nhcard : 21 = Fintype.card \u03b1\ni : \u03b2\nhG : #(\u03b2_solved i) \u2264 6\nh... | false | true | false | 1.3189 |
compfiles_Imo2001P4 | compfiles | Copyright (c) 2025 the Compfiles Contributers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Tan
-/
import Mathlib
/-!
# International Mathematical Olympiad 2001, Problem 4
Let $n > 1$ be an odd integer and let $c_1, c_2, \dots, c_n$ be integers. For
each ... | /- | /-
Copyright (c) 2025 the Compfiles Contributers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Tan
-/
import Mathlib
/-!
# International Mathematical Olympiad 2001, Problem 4
Let $n > 1$ be an odd integer and let $c_1, c_2, \dots, c_n$ be integers. For
ea... | true | Copyright (c) 2025 the Compfiles Contributers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Tan
-/
import Mathlib
/-!
# International Mathematical Olympiad 2001, Problem 4
Let $n > 1$ be an odd integer and let $c_1, c_2, \dots, c_n$ be integers. For
each ... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo2001P4.lean"} | {"v4.21.0": {"is_valid": true, "has_sorry": false, "errors": [], "timeout_s": 600.0, "latency_s": 1.2014, "verified_at": "2026-03-26T18:17:49.309423+00:00"}} | true | true | false | 1.2014 |
compfiles_Imo2001P5 | 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 2001, Problem 5
Let `ABC` be a triangle. Let `AP` bisect `∠BAC` and let `BQ` bisect `∠ABC`,
with `P` on `BC` and `Q... | /- | /-
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 2001, Problem 5
Let `ABC` be a triangle. Let `AP` bisect `∠BAC` and let `BQ` bisect `∠ABC`,
with `P` on `BC` and... | 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 2001, Problem 5
Let `ABC` be a triangle. Let `AP` bisect `∠BAC` and let `BQ` bisect `∠ABC`,
with `P` on `BC` and `Q... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo2001P5.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["expected token", "invalid field 'BAC_eq', the environment does not contain 'Imo2001P5.Setup.BAC_eq'\n s\nhas type\n Setup X", "unsolved goals\nV : Type u_1\nX : Type u_2\ninst\u271d\u00b3 : NormedAddCommGroup V\ninst\u271d\u00b2 : InnerProductSpace \u211... | false | true | false | 1.0699 |
compfiles_Imo2001P6 | compfiles | Copyright (c) 2021 Sara Díaz Real. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sara Díaz Real
-/
import Mathlib
/-!
# International Mathematical Olympiad 2001, Problem 6
Let a, b, c, d be integers with a > b > c > d > 0. Suppose that
ac + bd = (a + b - c + d... | /- | /-
Copyright (c) 2021 Sara Díaz Real. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sara Díaz Real
-/
import Mathlib
/-!
# International Mathematical Olympiad 2001, Problem 6
Let a, b, c, d be integers with a > b > c > d > 0. Suppose that
ac + bd = (a + b - c ... | true | Copyright (c) 2021 Sara Díaz Real. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sara Díaz Real
-/
import Mathlib
/-!
# International Mathematical Olympiad 2001, Problem 6
Let a, b, c, d be integers with a > b > c > d > 0. Suppose that
ac + bd = (a + b - c + d... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo2001P6.lean"} | {"v4.21.0": {"is_valid": true, "has_sorry": false, "errors": [], "timeout_s": 120, "latency_s": 0.8572, "verified_at": "2026-03-30T14:47:10.340989+00:00"}} | true | true | false | 0.8572 |
compfiles_Imo2002P3 | compfiles | Copyright (c) 2025 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Tan
-/
import Mathlib
/-!
# International Mathematical Olympiad 2002, Problem 3
Find all pairs of positive integers m,n ≥ 3 for which
there exist infinitely many p... | /- | /-
Copyright (c) 2025 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Tan
-/
import Mathlib
/-!
# International Mathematical Olympiad 2002, Problem 3
Find all pairs of positive integers m,n ≥ 3 for which
there exist infinitely man... | true | Copyright (c) 2025 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Tan
-/
import Mathlib
/-!
# International Mathematical Olympiad 2002, Problem 3
Find all pairs of positive integers m,n ≥ 3 for which
there exist infinitely many p... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo2002P3.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["unknown tactic", "unsolved goals\ncase hp.H\nm : \u2115\nhm : 3 \u2264 m\n\u22a2 1 < m", "unsolved goals\ncase hpq\nm : \u2115\nhm : 3 \u2264 m\n\u22a2 degree 1 < (X ^ m + X).degree", "unknown tactic", "unsolved goals\ncase hp.H\nn : \u2115\nhn : 3 \u2264 ... | false | true | false | 3.2405 |
compfiles_Imo2002P5 | 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 2002, Problem 5
Determine all functions f : ℝ → ℝ such that
(f(x) + f(z))(f(y) + f(t)) = f(xy... | /- | /-
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 2002, Problem 5
Determine all functions f : ℝ → ℝ such that
(f(x) + f(z))(f(y) + f(t)) = f... | 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 2002, Problem 5
Determine all functions f : ℝ → ℝ such that
(f(x) + f(z))(f(y) + f(t)) = f(xy... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo2002P5.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["unknown tactic", "`grind` failed\ncase grind\nf : \u211d \u2192 \u211d\nhf : \u2200 (x y z t : \u211d), (f x + f z) * (f y + f t) = f (x * y - z * t) + f (x * t + y * z)\nh1 : \u2200 (x : \u211d), f x = f (-x)\ny : \u211d\nhy : \u2200 (x : \u211d), f x = y... | false | true | false | 3.0781 |
compfiles_Imo2003P1 | compfiles | Copyright (c) 2025 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ansar Azhdarov
-/
import Mathlib
/-!
# International Mathematical Olympiad 2003, Problem 1
Let A be a 101-element subset of S = {1,2,...10⁶}. Prove that
there exist numbe... | /- | /-
Copyright (c) 2025 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ansar Azhdarov
-/
import Mathlib
/-!
# International Mathematical Olympiad 2003, Problem 1
Let A be a 101-element subset of S = {1,2,...10⁶}. Prove that
there exist nu... | true | Copyright (c) 2025 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ansar Azhdarov
-/
import Mathlib
/-!
# International Mathematical Olympiad 2003, Problem 1
Let A be a 101-element subset of S = {1,2,...10⁶}. Prove that
there exist numbe... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo2003P1.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["unknown tactic", "unsolved goals\nA : Finset \u2115\n_AS : A \u2286 S\nAcard : A.card = 101\nk : \u2115\nh :\n k \u2264 100 \u2192\n \u2203 t \u2286 S, t.card = k \u2227 \u2200 x \u2208 t, \u2200 y \u2208 t, x \u2260 y \u2192 Disjoint {x_1 | \u2203 a \... | false | true | false | 0.1736 |
compfiles_Imo2003P2 | compfiles | Copyright (c) 2023 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 2003, Problem 2
Determine all pairs of positive integers (a,b) such that
a²/(2a... | /- | /-
Copyright (c) 2023 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 2003, Problem 2
Determine all pairs of positive integers (a,b) such that
a²/... | true | Copyright (c) 2023 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 2003, Problem 2
Determine all pairs of positive integers (a,b) such that
a²/(2a... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo2003P2.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["unknown tactic", "unsolved goals\nn : \u2124\nhn : 0 < n\nthis : 1 \u2264 n ^ 3\n\u22a2 1 < 8 * n ^ 3", "unsolved goals\nn : \u2124\nhn : 0 < n\n\u22a2 1 \u2264 n ^ 3", "unknown tactic", "unsolved goals\ncase mpr.intro.intro.intro.intro.intro.intro.intro\n... | false | true | false | 0.4945 |
compfiles_Imo2003P6 | 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, Zhiyi Luo
-/
import Mathlib
/-!
# International Mathematical Olympiad 2003, Problem 6
Let p be a prime number. Prove that there exists a prime number q
suc... | /- | /-
Copyright (c) 2023 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Renshaw, Zhiyi Luo
-/
import Mathlib
/-!
# International Mathematical Olympiad 2003, Problem 6
Let p be a prime number. Prove that there exists a prime number q
... | 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, Zhiyi Luo
-/
import Mathlib
/-!
# International Mathematical Olympiad 2003, Problem 6
Let p be a prime number. Prove that there exists a prime number q
suc... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo2003P6.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["unknown tactic", "type mismatch\n Nat.mod_eq_iff_lt ?m.85859\nhas type\n ?m.85858 % ?m.85857 = ?m.85858 \u2194 ?m.85858 < ?m.85857 : Prop\nbut is expected to have type\n 1 % (p - 1) = 1 : Prop", "unsolved goals\np : \u2115\nhp : Nat.Prime p\np_odd : p %... | false | true | false | 1.3029 |
compfiles_Imo2004P2 | 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 2004, Problem 2
Find all polynomials P with real coefficients such that
for all reals a,b,c such tha... | /- | /-
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 2004, Problem 2
Find all polynomials P with real coefficients such that
for all reals a,b,c such ... | 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 2004, Problem 2
Find all polynomials P with real coefficients such that
for all reals a,b,c such tha... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo2004P2.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["unknown tactic", "unsolved goals\ncase h.a\nP : \u211d[X]\nhabc :\n \u2200 (a b c : \u211d), a * b + b * c + c * a = 0 \u2192 eval (a - b) P + eval (b - c) P + eval (c - a) P = 2 * eval (a + b + c) P\nhPaPbPc :\n \u2200 (Pa Pb Pc : \u211d[X]),\n Pa * ... | false | true | false | 0.6993 |
compfiles_Imo2004P6 | compfiles | Copyright (c) 2021 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors:
-/
import Mathlib
/-!
# International Mathematical Olympiad 2004, Problem 6
We call a positive integer *alternating* if every two consecutive
digits in its decimal represe... | /- | /-
Copyright (c) 2021 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors:
-/
import Mathlib
/-!
# International Mathematical Olympiad 2004, Problem 6
We call a positive integer *alternating* if every two consecutive
digits in its decimal repr... | false | null | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo2004P6.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": true, "errors": ["invalid field 'IsChain', the environment does not contain 'List.IsChain'\n n.digits 10\nhas type\n List \u2115"], "timeout_s": 600.0, "latency_s": 0.0364, "verified_at": "2026-03-26T18:18:28.478311+00:00"}} | false | true | true | 0.0364 |
compfiles_Imo2005P2 | 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 2005, Problem 2
Let $a_1, a_2, \dots$ be a sequence of integers with infinitely many positive and n... | /- | /-
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 2005, Problem 2
Let $a_1, a_2, \dots$ be a sequence of integers with infinitely many positive an... | 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 2005, Problem 2
Let $a_1, a_2, \dots$ be a sequence of integers with infinitely many positive and n... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo2005P2.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["unexpected token '_'; expected ']'", "failed to synthesize\n SetLike (Finset \u2124) \u2124\n\nAdditional diagnostic information may be available using the `set_option diagnostics true` command.", "failed to synthesize\n SetLike (Finset \u2124) \u2124\n\... | false | true | false | 4.3216 |
compfiles_Imo2005P3 | compfiles | Copyright (c) 2021 Manuel Candales. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Manuel Candales
-/
import Mathlib
/-!
# International Mathematical Olympiad 2005, Problem 3
Let `x`, `y` and `z` be positive real numbers such that `xyz ≥ 1`. Prove that:
`(x^5 - x^2)... | /- | /-
Copyright (c) 2021 Manuel Candales. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Manuel Candales
-/
import Mathlib
/-!
# International Mathematical Olympiad 2005, Problem 3
Let `x`, `y` and `z` be positive real numbers such that `xyz ≥ 1`. Prove that:
`(x^5 - x... | true | Copyright (c) 2021 Manuel Candales. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Manuel Candales
-/
import Mathlib
/-!
# International Mathematical Olympiad 2005, Problem 3
Let `x`, `y` and `z` be positive real numbers such that `xyz ≥ 1`. Prove that:
`(x^5 - x^2)... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo2005P3.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["unsolved goals\nx y z : \u211d\nhx : x > 0\nhy : y > 0\nhz : z > 0\nh : x * y * z \u2265 1\nkey :\n (x ^ 5 - x ^ 2) / (x ^ 5 + y ^ 2 + z ^ 2) - (x ^ 5 - x ^ 2 * 1) / (x ^ 3 * (x ^ 2 + y ^ 2 + z ^ 2)) =\n (x ^ 3 - 1) ^ 2 * x ^ 2 * (y ^ 2 + z ^ 2) / ((x ... | false | true | false | 3.3114 |
compfiles_Imo2005P4 | compfiles | Copyright (c) 2021 Heather Macbeth. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Heather Macbeth
-/
import Mathlib
/-!
# Intertional Mathematical Olympiad 2005, Problem 4
Determine all positive integers relatively prime to all the terms of the infinite sequence
`... | /- | /-
Copyright (c) 2021 Heather Macbeth. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Heather Macbeth
-/
import Mathlib
/-!
# Intertional Mathematical Olympiad 2005, Problem 4
Determine all positive integers relatively prime to all the terms of the infinite sequenc... | true | Copyright (c) 2021 Heather Macbeth. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Heather Macbeth
-/
import Mathlib
/-!
# Intertional Mathematical Olympiad 2005, Problem 4
Determine all positive integers relatively prime to all the terms of the infinite sequence
`... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo2005P4.lean"} | {"v4.21.0": {"is_valid": true, "has_sorry": false, "errors": [], "timeout_s": 120, "latency_s": 0.7044, "verified_at": "2026-03-30T14:47:33.469843+00:00"}} | true | true | false | 0.7044 |
compfiles_Imo2006P3 | 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 2006, Problem 3
Determine the least real number $M$ such that
$$
\left| ab(a^2 - b^2) + bc(b^2 - c^2) + ca(c^2 - a^2) ... | /- | /-
Copyright (c) 2021 Tian Chen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tian Chen
-/
import Mathlib
/-!
# International Mathematical Olympiad 2006, Problem 3
Determine the least real number $M$ such that
$$
\left| ab(a^2 - b^2) + bc(b^2 - c^2) + ca(c^2 - a^... | 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 2006, Problem 3
Determine the least real number $M$ such that
$$
\left| ab(a^2 - b^2) + bc(b^2 - c^2) + ca(c^2 - a^2) ... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo2006P3.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["function expected at\n sqrt\nterm has type\n ?m.30340", "failed to prove positivity/nonnegativity/nonzeroness", "function expected at\n sqrt\nterm has type\n x\u271d", "unknown identifier 'sq_sqrt'", "unsolved goals\nx\u271d : Sort u_1\nsqrt : x\u271d\... | false | true | false | 3.1584 |
compfiles_Imo2006P4 | compfiles | Copyright (c) 2025 Project Numina. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Project Numina Contributors
-/
import Mathlib
/-!
# International Mathematical Olympiad 2006, Problem 4
Determine all pairs $(x, y)$ of integers satisfying the equation $$ 1+2^{x}+2^... | /- | /-
Copyright (c) 2025 Project Numina. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Project Numina Contributors
-/
import Mathlib
/-!
# International Mathematical Olympiad 2006, Problem 4
Determine all pairs $(x, y)$ of integers satisfying the equation $$ 1+2^{x}... | true | Copyright (c) 2025 Project Numina. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Project Numina Contributors
-/
import Mathlib
/-!
# International Mathematical Olympiad 2006, Problem 4
Determine all pairs $(x, y)$ of integers satisfying the equation $$ 1+2^{x}+2^... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo2006P4.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["unknown tactic", "tactic 'apply' failed, could not unify the conclusion of `@add_lt_add_right`\n ?b + ?a < ?c + ?a\nwith the goal\n 1 + 2 ^ x < 1 + 1\n\nNote: The full type of `@add_lt_add_right` is\n \u2200 {\u03b1 : Type ?u.10042} [inst : Add \u03b1] ... | false | true | false | 0.4049 |
compfiles_Imo2006P5 | compfiles | Copyright (c) 2022 Violeta Hernández Palacios. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Violeta Hernández Palacios
-/
import Mathlib
/-!
# International Mathematical Olympiad 2006, Problem 5
Let $P(x)$ be a polynomial of degree $n>1$ with integer coefficients... | /- | /-
Copyright (c) 2022 Violeta Hernández Palacios. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Violeta Hernández Palacios
-/
import Mathlib
/-!
# International Mathematical Olympiad 2006, Problem 5
Let $P(x)$ be a polynomial of degree $n>1$ with integer coefficie... | true | Copyright (c) 2022 Violeta Hernández Palacios. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Violeta Hernández Palacios
-/
import Mathlib
/-!
# International Mathematical Olympiad 2006, Problem 5
Let $P(x)$ be a polynomial of degree $n>1$ with integer coefficients... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo2006P5.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["unknown tactic", "unsolved goals\na b c d : \u2124\nhne : a \u2260 b\nh\u2081 : (c - a).natAbs = (d - b).natAbs\nh\u2082 : (c - b).natAbs = (d - a).natAbs\n\u22a2 a + b = c + d", "function expected at\n periodicPts\nterm has type\n ?m.827", "function exp... | false | true | false | 0.4624 |
compfiles_Imo2007P1 | compfiles | Copyright (c) 2023 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 2007, Problem 1
Real numbers a₁, a₂, ..., aₙ are fixed. For each 1 ≤ i ≤ n,
we let dᵢ = max {aⱼ : 1 ... | /- | /-
Copyright (c) 2023 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 2007, Problem 1
Real numbers a₁, a₂, ..., aₙ are fixed. For each 1 ≤ i ≤ n,
we let dᵢ = max {aⱼ :... | true | Copyright (c) 2023 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 2007, Problem 1
Real numbers a₁, a₂, ..., aₙ are fixed. For each 1 ≤ i ≤ n,
we let dᵢ = max {aⱼ : 1 ... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo2007P1.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["unknown constant 'Finite.le_ciSup'", "unknown constant 'Finite.le_ciSup'", "unknown constant 'Finite.le_ciSup'", "unknown constant 'Finite.ciInf_le'", "unknown constant 'Finite.le_ciSup'"], "timeout_s": 600.0, "latency_s": 0.8428, "verified_at": "2026-03-2... | false | true | false | 0.8428 |
compfiles_Imo2007P5 | compfiles | Copyright (c) 2023 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Gian Sanjaya
-/
import Mathlib
/-!
# International Mathematical Olympiad 2007, Problem 5
Let a and b be positive integers. Show that if 4ab - 1 divides (4a² - 1)²
then a ... | /- | /-
Copyright (c) 2023 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Gian Sanjaya
-/
import Mathlib
/-!
# International Mathematical Olympiad 2007, Problem 5
Let a and b be positive integers. Show that if 4ab - 1 divides (4a² - 1)²
then... | true | Copyright (c) 2023 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Gian Sanjaya
-/
import Mathlib
/-!
# International Mathematical Olympiad 2007, Problem 5
Let a and b be positive integers. Show that if 4ab - 1 divides (4a² - 1)²
then a ... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo2007P5.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["unknown identifier 'mul_lt_mul_iff_right\u2080'", "unsolved goals\na : \u2115\nh : 0 < a\nb : \u2115\nh0 : a < b\nt c : \u2124\nh1 : (t * \u2191a - 1) ^ 2 = (t * \u2191b - 1) * (t * c - 1)\nht : 1 < t\nh2 : 0 < t\nx y : \u2124\n\u22a2 x < y \u2194 t * x < ... | false | true | false | 0.7082 |
compfiles_Imo2008P2 | compfiles | Copyright (c) 2021 Manuel Candales. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Manuel Candales
-/
import Mathlib
/-!
# International Mathematical Olympiad 2008, Problem 2
(a) Prove that
```
x^2 / (x-1)^2 + y^2 / (y-1)^2 + z^2 / (z-1)^2 ≥ 1
... | /- | /-
Copyright (c) 2021 Manuel Candales. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Manuel Candales
-/
import Mathlib
/-!
# International Mathematical Olympiad 2008, Problem 2
(a) Prove that
```
x^2 / (x-1)^2 + y^2 / (y-1)^2 + z^2 / (z-1)^2 ≥ 1... | true | Copyright (c) 2021 Manuel Candales. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Manuel Candales
-/
import Mathlib
/-!
# International Mathematical Olympiad 2008, Problem 2
(a) Prove that
```
x^2 / (x-1)^2 + y^2 / (y-1)^2 + z^2 / (z-1)^2 ≥ 1
... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo2008P2.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["unknown identifier 'field'", "unsolved goals\ncase h.intro.intro\nx y z : \u211d\nh : x * y * z = 1\nright\u271d : z \u2260 0\nhx : x \u2260 0\nhy : y \u2260 0\nthis : z * (y * x) = 1\n\u22a2 z = y\u207b\u00b9 / x", "unknown identifier 'field'", "simp made... | false | true | false | 3.0746 |
compfiles_Imo2008P3 | compfiles | Copyright (c) 2021 Manuel Candales. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Manuel Candales
-/
import Mathlib
/-!
# International Mathematical Olympiad 2008, Problem 3
Prove that there exist infinitely many positive integers `n` such that `n^2 + 1` has a prim... | /- | /-
Copyright (c) 2021 Manuel Candales. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Manuel Candales
-/
import Mathlib
/-!
# International Mathematical Olympiad 2008, Problem 3
Prove that there exist infinitely many positive integers `n` such that `n^2 + 1` has a p... | true | Copyright (c) 2021 Manuel Candales. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Manuel Candales
-/
import Mathlib
/-!
# International Mathematical Olympiad 2008, Problem 3
Prove that there exist infinitely many positive integers `n` such that `n^2 + 1` has a prim... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo2008P3.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["unknown tactic", "function expected at\n sqrt\nterm has type\n ?m.251", "unsolved goals\nx\u271d : Sort u_1\nsqrt : x\u271d\np : \u2115\nhpp : Nat.Prime p\nhp_mod_4_eq_1 : p \u2261 1 [MOD 4]\nhp_gt_20 : p > 20\nthis : Fact (Nat.Prime p)\nhp_mod_4_ne_3 : ... | false | true | false | 0.7055 |
compfiles_Imo2008P4 | compfiles | Copyright (c) 2023 Gian Sanjaya. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Gian Sanjaya
-/
import Mathlib
/-!
# International Mathematical Olympiad 2008, Problem 4
Determine all functions f from the positive reals to the positive reals
such that
(f(w)² + ... | /- | /-
Copyright (c) 2023 Gian Sanjaya. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Gian Sanjaya
-/
import Mathlib
/-!
# International Mathematical Olympiad 2008, Problem 4
Determine all functions f from the positive reals to the positive reals
such that
(f(w)²... | true | Copyright (c) 2023 Gian Sanjaya. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Gian Sanjaya
-/
import Mathlib
/-!
# International Mathematical Olympiad 2008, Problem 4
Determine all functions f from the positive reals to the positive reals
such that
(f(w)² + ... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo2008P4.lean"} | {"v4.21.0": {"is_valid": true, "has_sorry": false, "errors": [], "timeout_s": 600.0, "latency_s": 2.3363, "verified_at": "2026-03-26T18:18:34.307294+00:00"}} | true | true | false | 2.3363 |
compfiles_Imo2008P5 | 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 2008, Problem 5
Let n and k be positive integers with k ≥ n and k - n an even number.
There are 2n lamps labe... | /- | /-
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 2008, Problem 5
Let n and k be positive integers with k ≥ n and k - n an even number.
There are 2n lamps l... | 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 2008, Problem 5
Let n and k be positive integers with k ≥ n and k - n an even number.
There are 2n lamps labe... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo2008P5.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["unknown tactic", "unsolved goals\ncase pos.mp\nn k : \u2115\nf g : Fin k \u2192 Fin (2 * n)\nhg : \u2200 (j : Fin k), \u2191(g j) = if \u2191(f j) < n then \u2191(f j) else \u2191(f j) - n\ni : \u2115\nhi : i < n\nj : Fin k\nh : \u2191(f j) < n\nhj : \u219... | false | true | false | 1.1103 |
compfiles_Imo2009P5 | compfiles | Copyright (c) 2023 Gian Sanjaya. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Gian Sanjaya
-/
import Mathlib
/-!
# International Mathematical Olympiad 2009, Problem 5
Determine all functions f: ℤ>0 → ℤ>0 such that for all positive integers a and b,
the numbers
... | /- | /-
Copyright (c) 2023 Gian Sanjaya. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Gian Sanjaya
-/
import Mathlib
/-!
# International Mathematical Olympiad 2009, Problem 5
Determine all functions f: ℤ>0 → ℤ>0 such that for all positive integers a and b,
the number... | true | Copyright (c) 2023 Gian Sanjaya. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Gian Sanjaya
-/
import Mathlib
/-!
# International Mathematical Olympiad 2009, Problem 5
Determine all functions f: ℤ>0 → ℤ>0 such that for all positive integers a and b,
the numbers
... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo2009P5.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["unknown tactic", "unsolved goals\nf : \u2115 \u2192 \u2115\n\u22a2 (f = fun x => x) \u2192\n (\u2200 (x y : \u2115), f (y + f x) \u2264 f y + x) \u2227 (\u2200 (x y : \u2115), x \u2264 f y + f (y + f x)) \u2227 \u2200 (x y : \u2115), f y \u2264 f (y + f... | false | true | false | 0.2897 |
compfiles_Imo2009P6 | 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 2009, Problem 6
Let a₁, a₂, ..., aₙ be distinct positive integers and let M
be a set of n - 1 po... | /- | /-
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 2009, Problem 6
Let a₁, a₂, ..., aₙ be distinct positive integers and let M
be a set of n - 1... | false | null | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo2009P6.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": true, "errors": ["unknown tactic", "unknown tactic", "unsolved goals\nm n : \u2115\nf : Equiv.Perm (Fin m)\nh : m \u2264 n\nx : Fin n\nh1 : \u2191x < m\n\u22a2 \u2191(f \u27e8\u2191x, h1\u27e9) < n", "unknown tactic", "unsolved goals\nn : \u2115\nih :\n \u2200 m < n,\n 0... | false | true | true | 1.7777 |
compfiles_Imo2010P1 | compfiles | Copyright (c) 2023 David Renshaw. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Renshaw, Gian Sanjaya
-/
import Mathlib
/-!
# International Mathematical Olympiad 2010, Problem 1
Determine all functions f : ℝ → ℝ such that for all x,y ∈ ℝ,
f(... | /- | /-
Copyright (c) 2023 David Renshaw. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Renshaw, Gian Sanjaya
-/
import Mathlib
/-!
# International Mathematical Olympiad 2010, Problem 1
Determine all functions f : ℝ → ℝ such that for all x,y ∈ 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, Gian Sanjaya
-/
import Mathlib
/-!
# International Mathematical Olympiad 2010, Problem 1
Determine all functions f : ℝ → ℝ such that for all x,y ∈ ℝ,
f(... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo2010P1.lean"} | {"v4.21.0": {"is_valid": true, "has_sorry": false, "errors": [], "timeout_s": 600.0, "latency_s": 0.1876, "verified_at": "2026-03-26T18:18:35.020419+00:00"}} | true | true | false | 0.1876 |
compfiles_Imo2010P3 | compfiles | Copyright (c) 2023 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors:
-/
import Mathlib
/-!
# International Mathematical Olympiad 2010, Problem 3
Determine all functions g : ℤ>0 → ℤ>0 such that
(g(m) + n)(g(n) + m)
is alway... | /- | /-
Copyright (c) 2023 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors:
-/
import Mathlib
/-!
# International Mathematical Olympiad 2010, Problem 3
Determine all functions g : ℤ>0 → ℤ>0 such that
(g(m) + n)(g(n) + m)
is al... | false | null | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo2010P3.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": true, "errors": [], "timeout_s": 600.0, "latency_s": 0.272, "verified_at": "2026-03-26T18:18:35.105143+00:00"}} | false | true | true | 0.272 |
compfiles_Imo2010P5 | 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 2010, Problem 5
Each of the six boxes $B_1, B_2, B_3, B_4, B_5, B_6$ initially contains one coin.
The following two ... | /- | /-
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 2010, Problem 5
Each of the six boxes $B_1, B_2, B_3, B_4, B_5, B_6$ initially contains one coin.
The following t... | 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 2010, Problem 5
Each of the six boxes $B_1, B_2, B_3, B_4, B_5, B_6$ initially contains one coin.
The following two ... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo2010P5.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["function expected at\n single\nterm has type\n ?m.311", "function expected at\n single\nterm has type\n ?m.311", "function expected at\n swap\nterm has type\n ?m.1822", "function expected at\n single\nterm has type\n ?m.2063", "function expected at... | false | true | false | 0.9904 |
compfiles_Imo2010P6 | compfiles | Copyright (c) 2023 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Rydh
-/
import Mathlib
/-!
# International Mathematical Olympiad 2010, Problem 6
Let a₁, a₂, a₃, ... be a sequence of positive real numbers. Suppose that for some
... | /- | /-
Copyright (c) 2023 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Rydh
-/
import Mathlib
/-!
# International Mathematical Olympiad 2010, Problem 6
Let a₁, a₂, a₃, ... be a sequence of positive real numbers. Suppose that for so... | true | Copyright (c) 2023 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Rydh
-/
import Mathlib
/-!
# International Mathematical Olympiad 2010, Problem 6
Let a₁, a₂, a₃, ... be a sequence of positive real numbers. Suppose that for some
... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo2010P6.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["unknown constant 'Finset.nonempty_def'", "unknown identifier 'eq_of_le_of_ge'", "unexpected identifier; expected ']'", "no goals to be solved", "`grind` failed\ncase grind.1.1.1.1.1.1.1.1\na : \u2115 \u2192 \u211d\ns : \u2115\nhs_pos : 1 \u2264 s\nh : \u22... | false | true | false | 9.4193 |
compfiles_Imo2011P3 | compfiles | Copyright (c) 2021 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 2011, Problem 3
Let f : ℝ → ℝ be a function that satisfies
f(x + y) ≤ y * f(x) + f(f(x))
for all x and y... | /- | /-
Copyright (c) 2021 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 2011, Problem 3
Let f : ℝ → ℝ be a function that satisfies
f(x + y) ≤ y * f(x) + f(f(x))
for all x an... | true | Copyright (c) 2021 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 2011, Problem 3
Let f : ℝ → ℝ be a function that satisfies
f(x + y) ≤ y * f(x) + f(f(x))
for all x and y... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo2011P3.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["unknown identifier 'mul_lt_mul_iff_right\u2080'"], "timeout_s": 600.0, "latency_s": 0.4454, "verified_at": "2026-03-26T18:18:35.465978+00:00"}} | false | true | false | 0.4454 |
compfiles_Imo2011P5 | 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 2011, Problem 5
Let f be a function from the set of integers to the set
of positive integer... | /- | /-
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 2011, Problem 5
Let f be a function from the set of integers to the set
of positive inte... | 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 2011, Problem 5
Let f be a function from the set of integers to the set
of positive integer... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo2011P5.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["`grind` failed\ncase grind.2.2.2.2.2.2.1.1\nf : \u2124 \u2192 \u2124\nf_pos : \u2200 (n : \u2124), -1 * f n + 1 \u2264 0\nh : \u2200 (m n : \u2124), f (m + -1 * n) \u2223 f m - f n\nf_n_dvd_f_zero : \u2200 (n : \u2124), f n \u2223 f 0\nf_neg_n_eq_f_n : \u2... | false | true | false | 2.5431 |
compfiles_Imo2012P2 | compfiles | Copyright (c) 2023 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 2012, Problem 2
Let a₂, a₃, ..., aₙ be positive reals with product 1, where n ≥ 3.
Show that
(1 ... | /- | /-
Copyright (c) 2023 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 2012, Problem 2
Let a₂, a₃, ..., aₙ be positive reals with product 1, where n ≥ 3.
Show that
... | true | Copyright (c) 2023 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 2012, Problem 2
Let a₂, a₃, ..., aₙ be positive reals with product 1, where n ≥ 3.
Show that
(1 ... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo2012P2.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["Application type mismatch: In the application\n h' hw\u2081\nthe argument\n hw\u2081\nhas type\n 0 < w\u2081 : Prop\nbut is expected to have type\n \u2200 (i : Fin 2), 0 < ![w\u2081, w\u2082] i : Prop", "unsolved goals\nw\u2081 w\u2082 p\u2081 p\u2082 ... | false | true | false | 1.2679 |
compfiles_Imo2012P4 | compfiles | Copyright (c) 2023 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: spinylobster, ondanaoto, Seasawher
-/
import Mathlib
/-!
# International Mathematical Olympiad 2012, Problem 4
Determine all functions f : ℤ → ℤ such that for all integer... | /- | /-
Copyright (c) 2023 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: spinylobster, ondanaoto, Seasawher
-/
import Mathlib
/-!
# International Mathematical Olympiad 2012, Problem 4
Determine all functions f : ℤ → ℤ such that for all inte... | true | Copyright (c) 2023 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: spinylobster, ondanaoto, Seasawher
-/
import Mathlib
/-!
# International Mathematical Olympiad 2012, Problem 4
Determine all functions f : ℤ → ℤ such that for all integer... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo2012P4.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["`grind` failed\ncase grind.2\nx x' : \u2115\nh : Int.negSucc x + -1 * Int.negSucc x' + 1 \u2264 0\nh_1 : x \u2264 x'\nh_2 : \u00acx = x'\n\u22a2 False\n[grind] Goal diagnostics\n [facts] Asserted facts\n [prop] Int.negSucc x + -1 * Int.negSucc x' + 1 \... | false | true | false | 1.5067 |
compfiles_Imo2012P5 | compfiles | Copyright (c) 2026 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: tenthmascot
-/
import Mathlib
/-!
# International Mathematical Olympiad 2012, Problem 5
Let `ABC` be a triangle with `∠BCA = 90°`, and let `D` be the foot of the altitude ... | /- | /-
Copyright (c) 2026 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: tenthmascot
-/
import Mathlib
/-!
# International Mathematical Olympiad 2012, Problem 5
Let `ABC` be a triangle with `∠BCA = 90°`, and let `D` be the foot of the altitu... | true | Copyright (c) 2026 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: tenthmascot
-/
import Mathlib
/-!
# International Mathematical Olympiad 2012, Problem 5
Let `ABC` be a triangle with `∠BCA = 90°`, and let `D` be the foot of the altitude ... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo2012P5.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["function expected at\n Cospherical\nterm has type\n ?m.4900", "unknown identifier 'Simplex'", "`grind` failed\ncase grind\nV : Type u_3\nP : Type u_4\ninst : NormedAddCommGroup V\ninst_1 : InnerProductSpace \u211d V\ninst_2 : MetricSpace P\ninst_3 : Norm... | false | true | false | 2.9995 |
compfiles_Imo2012P6 | compfiles | Copyright (c) 2023 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Rydh, Codex
-/
import Mathlib
/-!
# International Mathematical Olympiad 2012, Problem 6
Find all positive integers n for which there exist non-negative
integers a₁... | /- | /-
Copyright (c) 2023 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Rydh, Codex
-/
import Mathlib
/-!
# International Mathematical Olympiad 2012, Problem 6
Find all positive integers n for which there exist non-negative
integers... | true | Copyright (c) 2023 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Rydh, Codex
-/
import Mathlib
/-!
# International Mathematical Olympiad 2012, Problem 6
Find all positive integers n for which there exist non-negative
integers a₁... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo2012P6.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["unsolved goals\ncase h\nn i : \u2115\n\u22a2 \u00aci = 0 \u2192 (i \u2264 n \u2194 i < n + 1)", "unknown tactic", "`grind` failed\ncase grind.1\nk : \u2115\na : \u2115 \u2192 \u2115\nha\u2081 : \u2211 i \u2208 Finset.Icc 1 (4 * k + 1), 1 / 2 ^ a i = 1\nha\... | false | true | false | 10.0924 |
compfiles_Imo2013P1 | compfiles | Copyright (c) 2021 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 2013, Problem 1
Prove that for any pair of positive integers k and n, there exist k positive integers
m₁, m₂, ... | /- | /-
Copyright (c) 2021 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 2013, Problem 1
Prove that for any pair of positive integers k and n, there exist k positive integers
m₁, m... | true | Copyright (c) 2021 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 2013, Problem 1
Prove that for any pair of positive integers k and n, there exist k positive integers
m₁, m₂, ... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo2013P1.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["unknown identifier 'field'", "tactic 'left' failed, left tactic works for inductive types with exactly 2 constructors\npk : \u2115\nhpk : \u2200 (n : \u2115+), \u2203 m, 1 + (2 ^ pk - 1) / \u2191\u2191n = \u220f i \u2208 Finset.range pk, (1 + 1 / \u2191\u2... | false | true | false | 1.5338 |
compfiles_Imo2013P5 | compfiles | Copyright (c) 2021 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 2013, Problem 5
Let ℚ>₀ be the set of positive rational numbers. Let f: ℚ>₀ → ℝ be a function satisfying
the ... | /- | /-
Copyright (c) 2021 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 2013, Problem 5
Let ℚ>₀ be the set of positive rational numbers. Let f: ℚ>₀ → ℝ be a function satisfying
t... | true | Copyright (c) 2021 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 2013, Problem 5
Let ℚ>₀ be the set of positive rational numbers. Let f: ℚ>₀ → ℝ be a function satisfying
the ... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo2013P5.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["unknown identifier 'mul_le_mul_iff_left\u2080'", "type mismatch\n add_le_add_right (H5 (a ^ N - x) h_big_enough) ?m.38723\nhas type\n \u2191(a ^ N - x) + ?m.38723 \u2264 f (a ^ N - x) + ?m.38723 : Prop\nbut is expected to have type\n f x + \u2191(a ^ N ... | false | true | false | 2.4727 |
compfiles_Imo2014P1 | 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 2014, Problem 1
Let a₀ < a₁ < a₂ < ... an infinite sequence of positive integers.
Prove that there exists a u... | /- | /-
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 2014, Problem 1
Let a₀ < a₁ < a₂ < ... an infinite sequence of positive integers.
Prove that there exists ... | 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 2014, Problem 1
Let a₀ < a₁ < a₂ < ... an infinite sequence of positive integers.
Prove that there exists a u... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo2014P1.lean"} | {"v4.21.0": {"is_valid": true, "has_sorry": false, "errors": [], "timeout_s": 120, "latency_s": 1.3522, "verified_at": "2026-03-30T14:49:07.594024+00:00"}} | true | true | false | 1.3522 |
compfiles_Imo2014P4 | 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 2014, Problem 4
Let P and Q be on segment BC of an acute triangle ABC such that
∠PAB = ∠BCA and ∠C... | /- | /-
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 2014, Problem 4
Let P and Q be on segment BC of an acute triangle ABC such that
∠PAB = ∠BCA and... | 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 2014, Problem 4
Let P and Q be on segment BC of an acute triangle ABC such that
∠PAB = ∠BCA and ∠C... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo2014P4.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["unknown constant 'Module.Basis.orientation'", "unknown tactic", "unsolved goals\nA B : Submodule \u211d (EuclideanSpace \u211d (Fin 2))\nhA : Module.finrank \u211d \u21a5A = 1\nh : A \u2294 B \u2260 \u22a4\nhAB : Module.finrank \u211d \u21a5(A \u2294 B) \u... | false | true | false | 9.642 |
compfiles_Imo2015P2 | compfiles | Copyright (c) 2023 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 2015, Problem 2
Determine all triples of positive integers a, b, c such that each of
ab - c, bc - a,... | /- | /-
Copyright (c) 2023 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 2015, Problem 2
Determine all triples of positive integers a, b, c such that each of
ab - c, bc -... | true | Copyright (c) 2023 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 2015, Problem 2
Determine all triples of positive integers a, b, c such that each of
ab - c, bc - a,... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo2015P2.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["unknown tactic", "unsolved goals\ncase intro\nm : \u2115\na : \u2124\nha' : 1 < a\nk : \u2124\nh : 2 ^ m \u2223 (2 * k + 1) ^ 2 - 1\nhk : a = 2 * k + 1\n\u22a2 2 ^ m \u2264 2 * (2 * k + 1) + 2", "unknown tactic", "unknown tactic", "unsolved goals\na b c : ... | false | true | false | 6.2143 |
compfiles_Imo2015P5 | 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 2015, Problem 5
Determine all functions f : ℝ → ℝ that satisfy
f(x + f(x + y)) + f(xy) = x + ... | /- | /-
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 2015, Problem 5
Determine all functions f : ℝ → ℝ that satisfy
f(x + f(x + y)) + f(xy) = x... | 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 2015, Problem 5
Determine all functions f : ℝ → ℝ that satisfy
f(x + f(x + y)) + f(xy) = x + ... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo2015P5.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["`grind` failed\ncase grind\nf : \u211d \u2192 \u211d\nhf : \u2200 (x y : \u211d), f (x + f (x + y)) + f (x * y) = x + f (x + y) + y * f x\nh1 : f (f 0) = 0\nh3 : \u2200 (x : \u211d), x + f (x + 1) \u2208 {t | f t = t}\nh4 : f 0 = 0\nx : \u211d\nh7 : f (-1)... | false | true | false | 35.2464 |
compfiles_Imo2015P6 | 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 2015, Problem 6
The sequence $a_1, a_2, \dots$ of integers satisfies the conditions
1. $1 ≤ a_j ≤ 2015$ for all $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 2015, Problem 6
The sequence $a_1, a_2, \dots$ of integers satisfies the conditions
1. $1 ≤ a_j ≤ 2015$ for all $j... | 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 2015, Problem 6
The sequence $a_1, a_2, \dots$ of integers satisfies the conditions
1. $1 ≤ a_j ≤ 2015$ for all $j ≥ ... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo2015P6.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["unknown tactic", "unsolved goals\ncase h\na : \u2115 \u2192 \u2124\nt\u271d t : \u2115\nih : \u2200 {z : \u2124}, z \u2208 pool a t \u2192 \u2203 u < t, \u2191u + a u = \u2191t + z\nz y : \u2124\ney : y - 1 = z\nh : y = a t\n\u22a2 t < t + 1 \u2227 \u2191t... | false | true | false | 0.9886 |
compfiles_Imo2016P4 | 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 2016, Problem 4
A set of positive integers is called *fragrant* if it contains
at least two elements... | /- | /-
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 2016, Problem 4
A set of positive integers is called *fragrant* if it contains
at least two eleme... | 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 2016, Problem 4
A set of positive integers is called *fragrant* if it contains
at least two elements... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo2016P4.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["unknown constant 'Set.ncard_range_of_injective'", "unsolved goals\na : \u2115\nb : \u2115+\nf : Fin \u2191b \u2192 \u2115+ := fun i => \u27e8P (a + \u2191i + 1), \u22ef\u27e9\nhset : Set.range f = {p | \u2203 i \u2264 b, \u2191p = P (a + \u2191i)}\nhf : Fu... | false | true | false | 7.4829 |
compfiles_Imo2016P5 | 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 2016, Problem 5
The equation
(x - 1)(x - 2) ... (x - 2016) = (x - 1)(x - 2) ... (x - 2016)
is written on ... | /- | /-
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 2016, Problem 5
The equation
(x - 1)(x - 2) ... (x - 2016) = (x - 1)(x - 2) ... (x - 2016)
is written ... | false | null | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo2016P5.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["unknown tactic", "unsolved goals\n\u22a2 \u2200 (n : \u2115), (n % 4 = 2 \u2228 n % 4 = 3) = \u00ac(n % 4 = 0 \u2228 n % 4 = 1)", "unsolved goals\ncase h\nhp : \u2200 (n : \u2115), (n % 4 = 2 \u2228 n % 4 = 3) = \u00ac(n % 4 = 0 \u2228 n % 4 = 1)\n\u22a2 {... | false | true | false | 0.1301 |
compfiles_Imo2017P1 | compfiles | Copyright (c) 2023 David Renshaw. 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 2017, Problem 1
For any integer a₀ > 1, define the sequence
aₙ₊₁ = √aₙ, if aₙ is a ... | /- | /-
Copyright (c) 2023 David Renshaw. 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 2017, Problem 1
For any integer a₀ > 1, define the sequence
aₙ₊₁ = √aₙ, if aₙ is... | true | Copyright (c) 2023 David Renshaw. 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 2017, Problem 1
For any integer a₀ > 1, define the sequence
aₙ₊₁ = √aₙ, if aₙ is a ... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo2017P1.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["unknown tactic", "unsolved goals\na : \u2115 \u2192 \u2115 \u2192 \u2115\nha\u2081 : \u2200 (x i : \u2115), 1 < x \u2192 if IsSquare (a x i) then a x (i + 1) = (a x i).sqrt else a x (i + 1) = a x i + 3\nx c i : \u2115\nhx\u2080 : 1 < x\nhi\u2080 : a x i = ... | false | true | false | 2.5603 |
compfiles_Imo2017P2 | compfiles | Copyright (c) 2023 Gian Cordana Sanjaya. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Gian Cordana Sanjaya
-/
import Mathlib
/-!
# International Mathematical Olympiad 2017, Problem 2
Find all functions `f : ℝ → ℝ` that satisfy
∀ x,y ∈ ℝ, f(f(x)f(y)) + f(x + y... | /- | /-
Copyright (c) 2023 Gian Cordana Sanjaya. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Gian Cordana Sanjaya
-/
import Mathlib
/-!
# International Mathematical Olympiad 2017, Problem 2
Find all functions `f : ℝ → ℝ` that satisfy
∀ x,y ∈ ℝ, f(f(x)f(y)) + f(x ... | true | Copyright (c) 2023 Gian Cordana Sanjaya. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Gian Cordana Sanjaya
-/
import Mathlib
/-!
# International Mathematical Olympiad 2017, Problem 2
Find all functions `f : ℝ → ℝ` that satisfy
∀ x,y ∈ ℝ, f(f(x)f(y)) + f(x + y... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo2017P2.lean"} | {"v4.21.0": {"is_valid": true, "has_sorry": false, "errors": [], "timeout_s": 600.0, "latency_s": 4.8312, "verified_at": "2026-03-26T18:19:24.526945+00:00"}} | true | true | false | 4.8312 |
compfiles_Imo2017P6 | 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 2017, Problem 6
A point (x,y) ∈ ℤ × ℤ is called primitive if gcd(x,y) = 1.
Let S be a finite set of primitive... | /- | /-
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 2017, Problem 6
A point (x,y) ∈ ℤ × ℤ is called primitive if gcd(x,y) = 1.
Let S be a finite set of primit... | false | null | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo2017P6.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": true, "errors": [], "timeout_s": 600.0, "latency_s": 0.0323, "verified_at": "2026-03-26T18:19:20.586116+00:00"}} | false | true | true | 0.0323 |
compfiles_Imo2018P2 | compfiles | Copyright (c) 2023 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Clayton Knittel
-/
import Mathlib
/-!
# International Mathematical Olympiad 2018, Problem 2
Determine all integers n ≥ 3 such that there exist real numbers
a₁, a₂, ..., a... | /- | /-
Copyright (c) 2023 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Clayton Knittel
-/
import Mathlib
/-!
# International Mathematical Olympiad 2018, Problem 2
Determine all integers n ≥ 3 such that there exist real numbers
a₁, a₂, ...... | true | Copyright (c) 2023 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Clayton Knittel
-/
import Mathlib
/-!
# International Mathematical Olympiad 2018, Problem 2
Determine all integers n ≥ 3 such that there exist real numbers
a₁, a₂, ..., a... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo2018P2.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["unknown constant 'Nat.exists_mul_mod_eq_one_of_coprime'", "invalid constructor \u27e8...\u27e9, expected type must be an inductive type \n ?m.4646", "no goals to be solved", "unknown identifier 'eq_zero_of_pow_eq_zero'", "unsolved goals\nn : \u2115\ninst\... | false | true | false | 6.1357 |
compfiles_Imo2018P3 | 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 2018, Problem 3
An anti-Pascal triangle is an equilateral triangular array of numbers such that,
except for t... | /- | /-
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 2018, Problem 3
An anti-Pascal triangle is an equilateral triangular array of numbers such that,
except fo... | false | null | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo2018P3.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": true, "errors": [], "timeout_s": 600.0, "latency_s": 0.091, "verified_at": "2026-03-26T18:19:22.217358+00:00"}} | false | true | true | 0.091 |
compfiles_Imo2018P5 | compfiles | Copyright (c) 2024 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors:
-/
import Mathlib
/-!
# International Mathematical Olympiad 2018, Problem 5
Let a₁, a₂, ... be an infinite sequence of positive integers.
Suppose that there is an integer... | /- | /-
Copyright (c) 2024 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors:
-/
import Mathlib
/-!
# International Mathematical Olympiad 2018, Problem 5
Let a₁, a₂, ... be an infinite sequence of positive integers.
Suppose that there is an inte... | false | null | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo2018P5.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": true, "errors": [], "timeout_s": 600.0, "latency_s": 0.0541, "verified_at": "2026-03-26T18:19:22.271626+00:00"}} | false | true | true | 0.0541 |
compfiles_Imo2019P1 | 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 2019, Problem 1
Let ℤ be the set of integers. Determine all functions f : ℤ → ℤ such that,
for all intege... | /- | /-
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 2019, Problem 1
Let ℤ be the set of integers. Determine all functions f : ℤ → ℤ such that,
for all int... | 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 2019, Problem 1
Let ℤ be the set of integers. Determine all functions f : ℤ → ℤ such that,
for all intege... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo2019P1.lean"} | {"v4.21.0": {"is_valid": true, "has_sorry": false, "errors": [], "timeout_s": 120, "latency_s": 0.8574, "verified_at": "2026-03-30T14:50:31.512443+00:00"}} | true | true | false | 0.8574 |
compfiles_Imo2019P2 | compfiles | Copyright (c) 2022 Joseph Myers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Myers
-/
import Mathlib
/-!
# International Mathematical Olympiad 2019, Problem 2
In triangle `ABC`, point `A₁` lies on side `BC` and point `B₁` lies on side `AC`. Let `P` and
`Q... | /- | /-
Copyright (c) 2022 Joseph Myers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Myers
-/
import Mathlib
/-!
# International Mathematical Olympiad 2019, Problem 2
In triangle `ABC`, point `A₁` lies on side `BC` and point `B₁` lies on side `AC`. Let `P` and... | true | Copyright (c) 2022 Joseph Myers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Myers
-/
import Mathlib
/-!
# International Mathematical Olympiad 2019, Problem 2
In triangle `ABC`, point `A₁` lies on side `BC` and point `B₁` lies on side `AC`. Let `P` and
`Q... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo2019P2.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["expected token", "function expected at\n finrank\nterm has type\n ?m.11801", "unknown identifier 'finBasisOfFinrankEq'", "unknown attribute [implicit_reducible]", "'P_ne_Q' is not a field of structure 'Imo2019q2Cfg'", "'sbtw_P_B\u2081_P\u2081' is not a f... | false | true | false | 4.1748 |
compfiles_Imo2019P4 | compfiles | Copyright (c) 2020 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn
-/
import Mathlib
/-!
# International Mathematical Olympiad 2019, Problem 4
Determine all positive integers n,k that satisfy the equation
k! = (2ⁿ - 2⁰)(2ⁿ - 2¹... | /- | /-
Copyright (c) 2020 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn
-/
import Mathlib
/-!
# International Mathematical Olympiad 2019, Problem 4
Determine all positive integers n,k that satisfy the equation
k! = (2ⁿ - 2⁰)(2ⁿ -... | true | Copyright (c) 2020 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn
-/
import Mathlib
/-!
# International Mathematical Olympiad 2019, Problem 4
Determine all positive integers n,k that satisfy the equation
k! = (2ⁿ - 2⁰)(2ⁿ - 2¹... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo2019P4.lean"} | {"v4.21.0": {"is_valid": true, "has_sorry": false, "errors": [], "timeout_s": 120, "latency_s": 1.5486, "verified_at": "2026-03-30T14:50:36.921541+00:00"}} | true | true | false | 1.5486 |
compfiles_Imo2020P2 | compfiles | Copyright (c) 2020 Joseph Myers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Myers, Yury Kudryashov
-/
import Mathlib
/-!
# International Mathematical Olympiad 2020, Problem 2
The real numbers `a`, `b`, `c`, `d` are such that `a ≥ b ≥ c ≥ d > 0` and `a + ... | /- | /-
Copyright (c) 2020 Joseph Myers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Myers, Yury Kudryashov
-/
import Mathlib
/-!
# International Mathematical Olympiad 2020, Problem 2
The real numbers `a`, `b`, `c`, `d` are such that `a ≥ b ≥ c ≥ d > 0` and `a... | true | Copyright (c) 2020 Joseph Myers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Myers, Yury Kudryashov
-/
import Mathlib
/-!
# International Mathematical Olympiad 2020, Problem 2
The real numbers `a`, `b`, `c`, `d` are such that `a ≥ b ≥ c ≥ d > 0` and `a + ... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo2020P2.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["unknown identifier 'geom_mean_le_arith_mean4_weighted'"], "timeout_s": 600.0, "latency_s": 1.7975, "verified_at": "2026-03-26T18:19:26.835814+00:00"}} | false | true | false | 1.7975 |
compfiles_Imo2020P3 | compfiles | Copyright (c) 2025 Joseph Myers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Myers
-/
import Mathlib
/-!
# International Mathematical Olympiad 2020, Problem 3
There are 4n pebbles of weights 1,2,3,...,4n. Each pebble is colored
in one of n colors and the... | /- | /-
Copyright (c) 2025 Joseph Myers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Myers
-/
import Mathlib
/-!
# International Mathematical Olympiad 2020, Problem 3
There are 4n pebbles of weights 1,2,3,...,4n. Each pebble is colored
in one of n colors and ... | false | null | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo2020P3.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": true, "errors": [], "timeout_s": 600.0, "latency_s": 0.0524, "verified_at": "2026-03-26T18:19:26.690609+00:00"}} | false | true | true | 0.0524 |
compfiles_Imo2020P4 | compfiles | Copyright (c) 2025 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Myers
-/
import Mathlib
/-!
# International Mathematical Olympiad 2020, Problem 4
There is an integer n > 1. There are n² stations on a slope of
a mountain, all at ... | /- | /-
Copyright (c) 2025 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Myers
-/
import Mathlib
/-!
# International Mathematical Olympiad 2020, Problem 4
There is an integer n > 1. There are n² stations on a slope of
a mountain, all ... | false | null | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo2020P4.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": true, "errors": ["invalid field 'IsChain', the environment does not contain 'List.IsChain'\n cars\nhas type\n List (Fin k)", "invalid field 'linkage', the environment does not contain 'Imo2020P4.Company.linkage'\n c\nhas type\n Company n k", "invalid field 'linkage', the... | false | true | true | 0.1501 |
compfiles_Imo2020P5 | compfiles | Copyright (c) 2024 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors:
-/
import Mathlib
/-!
# International Mathematical Olympiad 2020, Problem 5
A deck of n > 1 cards is given. A positive integer is written on
each card. The deck has the p... | /- | /-
Copyright (c) 2024 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors:
-/
import Mathlib
/-!
# International Mathematical Olympiad 2020, Problem 5
A deck of n > 1 cards is given. A positive integer is written on
each card. The deck has th... | false | null | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo2020P5.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": true, "errors": [], "timeout_s": 600.0, "latency_s": 0.0915, "verified_at": "2026-03-26T18:19:26.813650+00:00"}} | false | true | true | 0.0915 |
compfiles_Imo2020P6 | compfiles | Copyright (c) 2025 The Compfiles Authors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jovan Gerbscheid
-/
import Mathlib
/-!
# International Mathematical Olympiad 2020, Problem 6
Consider an integer n > 1, and a set S of n points in the plane
such that the dista... | /- | /-
Copyright (c) 2025 The Compfiles Authors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jovan Gerbscheid
-/
import Mathlib
/-!
# International Mathematical Olympiad 2020, Problem 6
Consider an integer n > 1, and a set S of n points in the plane
such that the di... | true | Copyright (c) 2025 The Compfiles Authors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jovan Gerbscheid
-/
import Mathlib
/-!
# International Mathematical Olympiad 2020, Problem 6
Consider an integer n > 1, and a set S of n points in the plane
such that the dista... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo2020P6.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["unknown tactic", "unknown identifier 'lineMap_le_lineMap_iff_of_lt''", "unsolved goals\ncase pos\n\u03b9 : Type u_3\nS : Finset \u03b9\nf : \u03b9 \u2192 \u211d\na b : \u211d\nhab : a < b\nn\u271d : \u2115\nn : \u2115 := n\u271d + 1\nhS : #({p \u2208 S | f... | false | true | false | 4.3308 |
compfiles_Imo2021P1 | compfiles | Copyright (c) 2021 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 2021, Problem 1
Let `n≥100` be an integer. Ivan writes the numbers `n, n+1,..., 2n` each on different cards.
H... | /- | /-
Copyright (c) 2021 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 2021, Problem 1
Let `n≥100` be an integer. Ivan writes the numbers `n, n+1,..., 2n` each on different cards... | true | Copyright (c) 2021 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 2021, Problem 1
Let `n≥100` be an integer. Ivan writes the numbers `n, n+1,..., 2n` each on different cards.
H... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo2021P1.lean"} | {"v4.21.0": {"is_valid": true, "has_sorry": false, "errors": [], "timeout_s": 120, "latency_s": 3.3249, "verified_at": "2026-03-30T14:50:51.301176+00:00"}} | true | true | false | 3.3249 |
compfiles_Imo2021P2 | compfiles | Copyright (c) 2023 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 2021, Problem 2
Let n be a natural number, and let x₁, ..., xₙ be real numbers.
Show that
∑ᵢ... | /- | /-
Copyright (c) 2023 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 2021, Problem 2
Let n be a natural number, and let x₁, ..., xₙ be real numbers.
Show that
... | true | Copyright (c) 2023 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 2021, Problem 2
Let n be a natural number, and let x₁, ..., xₙ be real numbers.
Show that
∑ᵢ... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo2021P2.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["`grind` failed\ncase grind\nf\u2081 f\u2082 : \u211d \u2192 \u211d\nh\u2081 : UnboundedAtPosInfinity f\u2081\nh\u2082 : UnboundedAtPosInfinity f\u2082\ny x\u2081 : \u211d\nhx\u2081 : \u2200 (t : \u211d), x\u2081 \u2264 t \u2192 y / 2 \u2264 f\u2081 t\nx\u2... | false | true | false | 2.6878 |
compfiles_Imo2021P3 | compfiles | Copyright (c) 2025 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Myers
-/
import Mathlib
/-!
# International Mathematical Olympiad 2021, Problem 3
Let D be an interior point of the acute triangle $ABC$ with
AB > AC so that ∠DAB =... | /- | /-
Copyright (c) 2025 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Myers
-/
import Mathlib
/-!
# International Mathematical Olympiad 2021, Problem 3
Let D be an interior point of the acute triangle $ABC$ with
AB > AC so that ∠DA... | false | null | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo2021P3.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["function expected at\n finrank\nterm has type\n ?m.595", "expected token"], "timeout_s": 600.0, "latency_s": 0.0963, "verified_at": "2026-03-26T18:19:27.146547+00:00"}} | false | true | false | 0.0963 |
compfiles_Imo2021P5 | compfiles | Copyright (c) 2025 Joseph Myers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Myers
-/
import Mathlib
/-!
# International Mathematical Olympiad 2021, Problem 5
Two squirrels, Bushy and Jumpy, have collected 2001 walnuts for winter.
Jumpy numbers the walnut... | /- | /-
Copyright (c) 2025 Joseph Myers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Myers
-/
import Mathlib
/-!
# International Mathematical Olympiad 2021, Problem 5
Two squirrels, Bushy and Jumpy, have collected 2001 walnuts for winter.
Jumpy numbers the wal... | false | null | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo2021P5.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": true, "errors": [], "timeout_s": 600.0, "latency_s": 0.0699, "verified_at": "2026-03-26T18:19:27.216580+00:00"}} | false | true | true | 0.0699 |
compfiles_Imo2021P6 | 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 2021, Problem 6
Let m ≥ 2 be an integer, A a finite set of integers (not necessarily
positive) and B₁, B₂, ..... | /- | /-
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 2021, Problem 6
Let m ≥ 2 be an integer, A a finite set of integers (not necessarily
positive) and B₁, B₂,... | false | null | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo2021P6.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": true, "errors": [], "timeout_s": 600.0, "latency_s": 0.0261, "verified_at": "2026-03-26T18:19:27.242785+00:00"}} | false | true | true | 0.0261 |
compfiles_Imo2022P1 | compfiles | Copyright (c) 2025 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Myers, Benpigchu
-/
import Mathlib
/-!
# International Mathematical Olympiad 2022, Problem 1
The bank of Oslo issues two types of coin: aluminum (denoted A)
and bron... | /- | /-
Copyright (c) 2025 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Myers, Benpigchu
-/
import Mathlib
/-!
# International Mathematical Olympiad 2022, Problem 1
The bank of Oslo issues two types of coin: aluminum (denoted A)
and b... | true | Copyright (c) 2025 The Compfiles Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Myers, Benpigchu
-/
import Mathlib
/-!
# International Mathematical Olympiad 2022, Problem 1
The bank of Oslo issues two types of coin: aluminum (denoted A)
and bron... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo2022P1.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["unexpected token '#'; expected term", "unknown tactic", "unsolved goals\nn : \u2115\nc : Row n\na b i : Fin (2 * n)\n\u22a2 ?m.5888 > 0", "unknown tactic", "unsolved goals\nn k : \u2115\nhk1 : 1 \u2264 k\nhkn : k \u2264 2 * n\nc : Row n\n\u22a2 k - 1 < 2 *... | false | true | false | 6.7927 |
compfiles_Imo2022P2 | 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 2022, Problem 2
Let ℝ+ be the set of positive real numbers.
Determine all functions f: ℝ+ → ℝ+ such that
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
/-!
# International Mathematical Olympiad 2022, Problem 2
Let ℝ+ be the set of positive real numbers.
Determine all functions f: ℝ+ → ℝ+ such that
f... | 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 2022, Problem 2
Let ℝ+ be the set of positive real numbers.
Determine all functions f: ℝ+ → ℝ+ such that
for ... | null | v4.29.0-rc6 | test | [
"competition",
"imo"
] | null | {"filename": "Imo2022P2.lean"} | {"v4.21.0": {"is_valid": false, "has_sorry": false, "errors": ["unknown identifier 'field'", "unsolved goals\ncase mk.mk\na : \u211d\nha : 0 < a\nb : \u211d\nhb : 0 < b\n\u22a2 2 \u2264 a / b + b / a", "`grind` failed\ncase grind\nf : { x // 0 < x } \u2192 { x // 0 < x }\nx : \u211d\nhx : 0 < x\ny : \u211d\nhy : 0 < y\... | false | true | false | 3.3747 |
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