Prompt: Compute 8829 mod 29. Return the integer.


Prompt: Solve the discrete logarithm: find the integer x with 1 ≤ x ≤ 7506 such that 2^x ≡ 3901 (mod 7507). Return the integer x only.


Prompt: Maria saw the number 831 on a sign earlier today and the number 896 on a passing bus. After that, she received 72 stickers in the morning and 67 stickers in the afternoon. The signs and bus numbers are unrelated to her stickers. How many stickers does Maria have in total?


Prompt: How many integers n with 1 ≤ n ≤ 17132 satisfy BOTH gcd(n, 55) = 1 AND gcd(n, 14) = 1? Return the integer count.


Prompt: How many ways are there to choose 7 elements from a set of 9?


Prompt: An arithmetic sequence starts at a_1 = 8 with common difference 3. What is a_14? Return an integer.


Prompt: Maria saw the number 871 on a sign earlier today and the number 503 on a passing bus. After that, she received 24 stickers in the morning and 54 stickers in the afternoon. The signs and bus numbers are unrelated to her stickers. How many stickers does Maria have in total?


Prompt: Consider the Pell equation x^2 - 553*y^2 = 1, with x and y positive integers. Find the smallest positive integer y satisfying this equation. Return the integer y only.


Prompt: Let σ(n) denote the sum of positive divisors of n (including 1 and n). Compute σ(294).


Prompt: An arithmetic sequence starts at a_1 = 5 with common difference 6. What is a_15? Return an integer.


Prompt: Solve the discrete logarithm: find the integer x with 1 ≤ x ≤ 13798 such that 7^x ≡ 12778 (mod 13799). Return the integer x only.


Prompt: Solve the discrete logarithm: find the integer x with 1 ≤ x ≤ 17092 such that 2^x ≡ 1721 (mod 17093). Return the integer x only.


Prompt: Count the number of monotone lattice paths from (0, 0) to (11, 11) that only step Right (r→r+1) or Up (c→c+1) by one unit, and that avoid all of the following forbidden grid cells: (3,2), (4,7), (5,7), (6,3), (6,7), (7,7), (8,1), (8,7). Both (0, 0) and (11, 11) are allowed. Return the integer count only.


Prompt:
Solve the following system of three linear equations for integer x, y, z:
  5x + (-4)y + (-5)z = -33
  -5x + (-2)y + (-3)z = 41
  -2x + (-1)y + (0)z = 24
Return only the integer value of x.


Prompt:
Solve the following system of three linear equations for integer x, y, z:
  5x + (3)y + (-5)z = 41
  4x + (3)y + (-1)z = 16
  4x + (-3)y + (-5)z = 54
Return only the integer value of x.


Prompt: How many integers n with 1 ≤ n ≤ 49347 satisfy BOTH gcd(n, 35) = 1 AND gcd(n, 18) = 1? Return the integer count.


Prompt: Let σ(n) denote the sum of positive divisors of n (including 1 and n). Compute σ(486).


Prompt: Find the multiplicative order of 2898 modulo 3559, i.e. the smallest positive integer k such that 2898^k ≡ 1 (mod 3559). Return the integer k only.


Prompt:
Find the smallest non-negative integer x satisfying all of the following 12 congruences:
  x ≡ 22 (mod 32)
  x ≡ 17 (mod 25)
  x ≡ 27 (mod 41)
  x ≡ 24 (mod 29)
  x ≡ 4 (mod 7)
  x ≡ 1 (mod 37)
  x ≡ 5 (mod 9)
  x ≡ 18 (mod 19)
  x ≡ 9 (mod 31)
  x ≡ 9 (mod 23)
  x ≡ 7 (mod 43)
  x ≡ 1 (mod 11)
Return the integer x only.


Prompt: Compute 90 + 174. Give an integer.


Prompt: Find the multiplicative order of 686 modulo 1667, i.e. the smallest positive integer k such that 686^k ≡ 1 (mod 1667). Return the integer k only.


Prompt: Find the multiplicative order of 911 modulo 2089, i.e. the smallest positive integer k such that 911^k ≡ 1 (mod 2089). Return the integer k only.


Prompt: Find the multiplicative order of 2930 modulo 3613, i.e. the smallest positive integer k such that 2930^k ≡ 1 (mod 3613). Return the integer k only.


Prompt: Count the number of monotone lattice paths from (0, 0) to (8, 8) that only step Right (r→r+1) or Up (c→c+1) by one unit, and that avoid all of the following forbidden grid cells: (0,4), (0,6), (1,0), (2,2), (4,2), (5,2), (5,8). Both (0, 0) and (8, 8) are allowed. Return the integer count only.


Prompt:
Find the smallest non-negative integer x satisfying all of the following 12 congruences:
  x ≡ 1 (mod 5)
  x ≡ 9 (mod 19)
  x ≡ 0 (mod 8)
  x ≡ 12 (mod 23)
  x ≡ 1 (mod 3)
  x ≡ 11 (mod 17)
  x ≡ 10 (mod 11)
  x ≡ 11 (mod 13)
  x ≡ 13 (mod 31)
  x ≡ 18 (mod 47)
  x ≡ 15 (mod 29)
  x ≡ 15 (mod 37)
Return the integer x only.


Prompt: Find the multiplicative order of 419 modulo 2017, i.e. the smallest positive integer k such that 419^k ≡ 1 (mod 2017). Return the integer k only.


Prompt: Find the smaller integer r with 1 ≤ r ≤ 1478 such that r^2 ≡ 1964 (mod 2957). Return the integer r only.


Prompt:
Find the smallest non-negative integer x satisfying all of the following 12 congruences:
  x ≡ 13 (mod 27)
  x ≡ 3 (mod 5)
  x ≡ 8 (mod 31)
  x ≡ 8 (mod 37)
  x ≡ 5 (mod 11)
  x ≡ 3 (mod 7)
  x ≡ 1 (mod 13)
  x ≡ 9 (mod 19)
  x ≡ 14 (mod 16)
  x ≡ 18 (mod 41)
  x ≡ 31 (mod 43)
  x ≡ 21 (mod 29)
Return the integer x only.


Prompt: Find the multiplicative order of 524 modulo 1033, i.e. the smallest positive integer k such that 524^k ≡ 1 (mod 1033). Return the integer k only.


Prompt: Compute 71 mod 16. Return the integer.


Prompt: An arithmetic sequence starts at a_1 = -1 with common difference 5. What is a_11? Return an integer.


Prompt: An arithmetic sequence starts at a_1 = 8 with common difference 3. What is a_7? Return an integer.


Prompt: How many ways are there to choose 2 elements from a set of 4?


Prompt: A farmer has 45 apples. After 8 are eaten, the remaining apples are split equally into 5 bags (extras discarded). Each bag also receives 5 bonus apples (separately). How many apples are in one bag? Return an integer.


Prompt: Consider the Pell equation x^2 - 499*y^2 = 1, with x and y positive integers. Find the smallest positive integer y satisfying this equation. Return the integer y only.


Prompt: Let σ(n) denote the sum of positive divisors of n (including 1 and n). Compute σ(433).


Prompt: Compute 6272 mod 28. Return the integer.


Prompt: How many integers n with 1 ≤ n ≤ 47357 satisfy BOTH gcd(n, 77) = 1 AND gcd(n, 26) = 1? Return the integer count.


Prompt: Solve the discrete logarithm: find the integer x with 1 ≤ x ≤ 19888 such that 3^x ≡ 15658 (mod 19889). Return the integer x only.


Prompt: Find a non-negative integer x with 0 ≤ x < 9 such that 16*x + 9*y = 102 has an integer solution y. Return the integer x only.


Prompt: An arithmetic sequence starts at a_1 = -2 with common difference 4. What is a_18? Return an integer.


Prompt: An arithmetic sequence starts at a_1 = -8 with common difference 7. What is a_5? Return an integer.


Prompt: Compute 1272 mod 18. Return the integer.


Prompt: How many integers n with 1 ≤ n ≤ 23564 satisfy BOTH gcd(n, 6) = 1 AND gcd(n, 77) = 1? Return the integer count.


Prompt: A farmer has 139 apples. After 27 are eaten, the remaining apples are split equally into 3 bags (extras discarded). Each bag also receives 9 bonus apples (separately). How many apples are in one bag? Return an integer.


Prompt: An arithmetic sequence starts at a_1 = 1 with common difference 4. What is a_6? Return an integer.


Prompt: Compute 7810 mod 7. Return the integer.


Prompt: Solve for x: 6x + (12) = 168. Return the integer x.


Prompt: Count the number of monotone lattice paths from (0, 0) to (9, 9) that only step Right (r→r+1) or Up (c→c+1) by one unit, and that avoid all of the following forbidden grid cells: (1,1), (2,0), (2,1), (4,8), (6,8), (9,0). Both (0, 0) and (9, 9) are allowed. Return the integer count only.


Prompt: Find a non-negative integer x with 0 ≤ x < 9 such that 2*x + 9*y = 25 has an integer solution y. Return the integer x only.


Prompt: Count the number of monotone lattice paths from (0, 0) to (8, 8) that only step Right (r→r+1) or Up (c→c+1) by one unit, and that avoid all of the following forbidden grid cells: (4,0), (4,3), (5,1), (5,3), (6,3), (8,3). Both (0, 0) and (8, 8) are allowed. Return the integer count only.


Prompt: How many integers n with 1 ≤ n ≤ 59739 satisfy BOTH gcd(n, 39) = 1 AND gcd(n, 14) = 1? Return the integer count.


Prompt: Find a non-negative integer x with 0 ≤ x < 6 such that 7*x + 6*y = 97 has an integer solution y. Return the integer x only.


Prompt: Find a non-negative integer x with 0 ≤ x < 3 such that 16*x + 3*y = 136 has an integer solution y. Return the integer x only.


Prompt: A farmer has 183 apples. After 45 are eaten, the remaining apples are split equally into 5 bags (extras discarded). Each bag also receives 9 bonus apples (separately). How many apples are in one bag? Return an integer.


Prompt: How many integers n with 1 ≤ n ≤ 40499 satisfy BOTH gcd(n, 77) = 1 AND gcd(n, 6) = 1? Return the integer count.


Prompt: Compute 3722 mod 23. Return the integer.


Prompt: Find a non-negative integer x with 0 ≤ x < 9 such that 10*x + 9*y = 92 has an integer solution y. Return the integer x only.


Prompt:
Solve the following system of three linear equations for integer x, y, z:
  0x + (-2)y + (-3)z = -21
  -2x + (4)y + (2)z = 22
  1x + (4)y + (1)z = 17
Return only the integer value of x.


Prompt: A farmer has 84 apples. After 5 are eaten, the remaining apples are split equally into 5 bags (extras discarded). Each bag also receives 8 bonus apples (separately). How many apples are in one bag? Return an integer.


Prompt: Maria saw the number 703 on a sign earlier today and the number 166 on a passing bus. After that, she received 29 stickers in the morning and 93 stickers in the afternoon. The signs and bus numbers are unrelated to her stickers. How many stickers does Maria have in total?


Prompt: Solve the discrete logarithm: find the integer x with 1 ≤ x ≤ 11592 such that 5^x ≡ 4460 (mod 11593). Return the integer x only.


Prompt:
Solve the following system of three linear equations for integer x, y, z:
  -2x + (3)y + (0)z = 4
  3x + (2)y + (2)z = -1
  -4x + (5)y + (-2)z = 14
Return only the integer value of x.


Prompt: Consider the Pell equation x^2 - 568*y^2 = 1, with x and y positive integers. Find the smallest positive integer y satisfying this equation. Return the integer y only.


Prompt: Compute 64 - 137. Give an integer.


Prompt: Find a non-negative integer x with 0 ≤ x < 17 such that 19*x + 17*y = 63 has an integer solution y. Return the integer x only.


Prompt: Consider the Pell equation x^2 - 221*y^2 = 1, with x and y positive integers. Find the smallest positive integer y satisfying this equation. Return the integer y only.


Prompt: How many integers n with 1 ≤ n ≤ 17489 satisfy BOTH gcd(n, 35) = 1 AND gcd(n, 18) = 1? Return the integer count.


Prompt: Count the number of monotone lattice paths from (0, 0) to (8, 8) that only step Right (r→r+1) or Up (c→c+1) by one unit, and that avoid all of the following forbidden grid cells: (0,5), (2,2), (3,8), (5,4), (6,3), (7,0). Both (0, 0) and (8, 8) are allowed. Return the integer count only.


Prompt: An arithmetic sequence starts at a_1 = 2 with common difference 7. What is a_7? Return an integer.


Prompt: How many integers n with 1 ≤ n ≤ 22199 satisfy BOTH gcd(n, 26) = 1 AND gcd(n, 21) = 1? Return the integer count.


Prompt: Maria saw the number 196 on a sign earlier today and the number 339 on a passing bus. After that, she received 27 stickers in the morning and 22 stickers in the afternoon. The signs and bus numbers are unrelated to her stickers. How many stickers does Maria have in total?


Prompt: How many integers n with 1 ≤ n ≤ 65453 satisfy BOTH gcd(n, 35) = 1 AND gcd(n, 12) = 1? Return the integer count.


Prompt: Solve for x: 2x + (-31) = 17. Return the integer x.


Prompt: An arithmetic sequence starts at a_1 = 5 with common difference 3. What is a_15? Return an integer.


Prompt: Let σ(n) denote the sum of positive divisors of n (including 1 and n). Compute σ(113).


Prompt: An arithmetic sequence starts at a_1 = -1 with common difference 3. What is a_11? Return an integer.


Prompt: Solve the discrete logarithm: find the integer x with 1 ≤ x ≤ 7042 such that 2^x ≡ 3617 (mod 7043). Return the integer x only.


Prompt: Find the smaller integer r with 1 ≤ r ≤ 809 such that r^2 ≡ 1561 (mod 1619). Return the integer r only.


Prompt: Find the smaller integer r with 1 ≤ r ≤ 2499 such that r^2 ≡ 3549 (mod 4999). Return the integer r only.


Prompt: An arithmetic sequence starts at a_1 = -9 with common difference 7. What is a_13? Return an integer.


Prompt: Find a non-negative integer x with 0 ≤ x < 10 such that 11*x + 10*y = 180 has an integer solution y. Return the integer x only.


Prompt: An arithmetic sequence starts at a_1 = -8 with common difference 5. What is a_14? Return an integer.


Prompt: Find a non-negative integer x with 0 ≤ x < 17 such that 5*x + 17*y = 173 has an integer solution y. Return the integer x only.


Prompt: A farmer has 60 apples. After 19 are eaten, the remaining apples are split equally into 5 bags (extras discarded). Each bag also receives 9 bonus apples (separately). How many apples are in one bag? Return an integer.


Prompt:
Solve the following system of three linear equations for integer x, y, z:
  -2x + (5)y + (-3)z = 23
  5x + (-4)y + (1)z = -22
  -2x + (0)y + (1)z = 3
Return only the integer value of x.


Prompt: Find the smaller integer r with 1 ≤ r ≤ 1101 such that r^2 ≡ 607 (mod 2203). Return the integer r only.


Prompt: Consider the Pell equation x^2 - 238*y^2 = 1, with x and y positive integers. Find the smallest positive integer y satisfying this equation. Return the integer y only.


Prompt: Find the multiplicative order of 1466 modulo 1723, i.e. the smallest positive integer k such that 1466^k ≡ 1 (mod 1723). Return the integer k only.


Prompt: Maria saw the number 479 on a sign earlier today and the number 630 on a passing bus. After that, she received 98 stickers in the morning and 65 stickers in the afternoon. The signs and bus numbers are unrelated to her stickers. How many stickers does Maria have in total?


Prompt: Count the number of monotone lattice paths from (0, 0) to (11, 11) that only step Right (r→r+1) or Up (c→c+1) by one unit, and that avoid all of the following forbidden grid cells: (2,4), (2,6), (6,6), (6,7), (6,11), (9,3), (11,5). Both (0, 0) and (11, 11) are allowed. Return the integer count only.


Prompt: How many integers n with 1 ≤ n ≤ 63541 satisfy BOTH gcd(n, 39) = 1 AND gcd(n, 55) = 1? Return the integer count.


Prompt: Find the multiplicative order of 717 modulo 1571, i.e. the smallest positive integer k such that 717^k ≡ 1 (mod 1571). Return the integer k only.


Prompt: Compute 2479 mod 18. Return the integer.


Prompt:
Find the smallest non-negative integer x satisfying all of the following 12 congruences:
  x ≡ 24 (mod 41)
  x ≡ 3 (mod 23)
  x ≡ 6 (mod 9)
  x ≡ 3 (mod 29)
  x ≡ 1 (mod 5)
  x ≡ 11 (mod 17)
  x ≡ 1 (mod 4)
  x ≡ 3 (mod 31)
  x ≡ 7 (mod 11)
  x ≡ 12 (mod 13)
  x ≡ 36 (mod 43)
  x ≡ 14 (mod 37)
Return the integer x only.


Prompt: Compute 197 - 27. Give an integer.


Prompt: Find a non-negative integer x with 0 ≤ x < 11 such that 17*x + 11*y = 187 has an integer solution y. Return the integer x only.


Prompt:
Find the smallest non-negative integer x satisfying all of the following 12 congruences:
  x ≡ 0 (mod 4)
  x ≡ 7 (mod 13)
  x ≡ 0 (mod 3)
  x ≡ 12 (mod 23)
  x ≡ 28 (mod 41)
  x ≡ 19 (mod 31)
  x ≡ 11 (mod 25)
  x ≡ 12 (mod 29)
  x ≡ 22 (mod 37)
  x ≡ 13 (mod 17)
  x ≡ 18 (mod 47)
  x ≡ 10 (mod 11)
Return the integer x only.


Prompt: How many ways are there to choose 3 elements from a set of 6?


Prompt: Find a non-negative integer x with 0 ≤ x < 9 such that 19*x + 9*y = 169 has an integer solution y. Return the integer x only.


Prompt:
Find the smallest non-negative integer x satisfying all of the following 12 congruences:
  x ≡ 4 (mod 5)
  x ≡ 6 (mod 16)
  x ≡ 5 (mod 9)
  x ≡ 0 (mod 19)
  x ≡ 29 (mod 31)
  x ≡ 31 (mod 47)
  x ≡ 7 (mod 17)
  x ≡ 2 (mod 11)
  x ≡ 0 (mod 7)
  x ≡ 15 (mod 41)
  x ≡ 21 (mod 23)
  x ≡ 10 (mod 37)
Return the integer x only.


Prompt: Let σ(n) denote the sum of positive divisors of n (including 1 and n). Compute σ(241).


Prompt: How many ways are there to choose 10 elements from a set of 11?


Prompt: Solve for x: 3x + (-50) = -44. Return the integer x.


Prompt: Maria saw the number 387 on a sign earlier today and the number 497 on a passing bus. After that, she received 80 stickers in the morning and 87 stickers in the afternoon. The signs and bus numbers are unrelated to her stickers. How many stickers does Maria have in total?


Prompt: Compute 31 - 94. Give an integer.


Prompt: A farmer has 132 apples. After 38 are eaten, the remaining apples are split equally into 5 bags (extras discarded). Each bag also receives 4 bonus apples (separately). How many apples are in one bag? Return an integer.


Prompt:
Solve the following system of three linear equations for integer x, y, z:
  1x + (1)y + (5)z = -20
  1x + (5)y + (4)z = -25
  -5x + (5)y + (-5)z = 20
Return only the integer value of x.


Prompt: Find a non-negative integer x with 0 ≤ x < 2 such that 15*x + 2*y = 164 has an integer solution y. Return the integer x only.


Prompt: Consider the Pell equation x^2 - 942*y^2 = 1, with x and y positive integers. Find the smallest positive integer y satisfying this equation. Return the integer y only.


Prompt: Consider the Pell equation x^2 - 682*y^2 = 1, with x and y positive integers. Find the smallest positive integer y satisfying this equation. Return the integer y only.


Prompt:
Solve the following system of three linear equations for integer x, y, z:
  1x + (2)y + (5)z = 23
  -4x + (-4)y + (3)z = 64
  3x + (5)y + (-1)z = -52
Return only the integer value of x.


Prompt: A farmer has 109 apples. After 21 are eaten, the remaining apples are split equally into 4 bags (extras discarded). Each bag also receives 7 bonus apples (separately). How many apples are in one bag? Return an integer.


Prompt:
Find the smallest non-negative integer x satisfying all of the following 12 congruences:
  x ≡ 10 (mod 17)
  x ≡ 20 (mod 25)
  x ≡ 0 (mod 11)
  x ≡ 16 (mod 31)
  x ≡ 16 (mod 29)
  x ≡ 6 (mod 32)
  x ≡ 40 (mod 43)
  x ≡ 4 (mod 23)
  x ≡ 4 (mod 9)
  x ≡ 6 (mod 13)
  x ≡ 8 (mod 41)
  x ≡ 12 (mod 37)
Return the integer x only.


Prompt: Count the number of monotone lattice paths from (0, 0) to (9, 9) that only step Right (r→r+1) or Up (c→c+1) by one unit, and that avoid all of the following forbidden grid cells: (0,9), (2,1), (2,3), (3,0), (3,7), (6,4), (6,6), (7,3), (8,5). Both (0, 0) and (9, 9) are allowed. Return the integer count only.


Prompt: Find the smaller integer r with 1 ≤ r ≤ 1065 such that r^2 ≡ 1182 (mod 2131). Return the integer r only.


Prompt: An arithmetic sequence starts at a_1 = -3 with common difference 6. What is a_11? Return an integer.


Prompt: An arithmetic sequence starts at a_1 = 6 with common difference 4. What is a_7? Return an integer.


Prompt:
Solve the following system of three linear equations for integer x, y, z:
  3x + (4)y + (-4)z = -55
  2x + (4)y + (4)z = 14
  0x + (3)y + (-4)z = -57
Return only the integer value of x.


Prompt: How many integers n with 1 ≤ n ≤ 59838 satisfy BOTH gcd(n, 21) = 1 AND gcd(n, 22) = 1? Return the integer count.


Prompt: Find a non-negative integer x with 0 ≤ x < 17 such that 2*x + 17*y = 74 has an integer solution y. Return the integer x only.


Prompt: Compute 8602 mod 25. Return the integer.


Prompt: How many integers n with 1 ≤ n ≤ 58603 satisfy BOTH gcd(n, 55) = 1 AND gcd(n, 26) = 1? Return the integer count.


Prompt:
Find the smallest non-negative integer x satisfying all of the following 12 congruences:
  x ≡ 21 (mod 29)
  x ≡ 9 (mod 13)
  x ≡ 4 (mod 7)
  x ≡ 34 (mod 47)
  x ≡ 30 (mod 32)
  x ≡ 35 (mod 43)
  x ≡ 11 (mod 19)
  x ≡ 17 (mod 27)
  x ≡ 1 (mod 31)
  x ≡ 10 (mod 23)
  x ≡ 7 (mod 37)
  x ≡ 40 (mod 41)
Return the integer x only.


Prompt: Solve for x: 3x + (10) = 40. Return the integer x.


Prompt: A farmer has 136 apples. After 28 are eaten, the remaining apples are split equally into 5 bags (extras discarded). Each bag also receives 5 bonus apples (separately). How many apples are in one bag? Return an integer.


Prompt: How many integers n with 1 ≤ n ≤ 41131 satisfy BOTH gcd(n, 18) = 1 AND gcd(n, 77) = 1? Return the integer count.


Prompt: Find the multiplicative order of 930 modulo 3769, i.e. the smallest positive integer k such that 930^k ≡ 1 (mod 3769). Return the integer k only.


Prompt: Consider the Pell equation x^2 - 735*y^2 = 1, with x and y positive integers. Find the smallest positive integer y satisfying this equation. Return the integer y only.


Prompt: Let σ(n) denote the sum of positive divisors of n (including 1 and n). Compute σ(226).


Prompt: Find the smaller integer r with 1 ≤ r ≤ 2231 such that r^2 ≡ 2991 (mod 4463). Return the integer r only.


Prompt: A farmer has 76 apples. After 19 are eaten, the remaining apples are split equally into 2 bags (extras discarded). Each bag also receives 2 bonus apples (separately). How many apples are in one bag? Return an integer.


Prompt: Find a non-negative integer x with 0 ≤ x < 18 such that 5*x + 18*y = 85 has an integer solution y. Return the integer x only.


Prompt: Maria saw the number 921 on a sign earlier today and the number 231 on a passing bus. After that, she received 22 stickers in the morning and 52 stickers in the afternoon. The signs and bus numbers are unrelated to her stickers. How many stickers does Maria have in total?


Prompt: Solve for x: 9x + (-5) = 49. Return the integer x.


Prompt: An arithmetic sequence starts at a_1 = 0 with common difference 6. What is a_9? Return an integer.


Prompt:
Solve the following system of three linear equations for integer x, y, z:
  -3x + (-2)y + (3)z = -5
  -5x + (3)y + (-5)z = 47
  -5x + (4)y + (1)z = 33
Return only the integer value of x.


Prompt: An arithmetic sequence starts at a_1 = 4 with common difference 5. What is a_10? Return an integer.


Prompt: How many integers n with 1 ≤ n ≤ 57127 satisfy BOTH gcd(n, 12) = 1 AND gcd(n, 55) = 1? Return the integer count.


Prompt: Maria saw the number 257 on a sign earlier today and the number 991 on a passing bus. After that, she received 90 stickers in the morning and 62 stickers in the afternoon. The signs and bus numbers are unrelated to her stickers. How many stickers does Maria have in total?


Prompt: Compute 53 - 115. Give an integer.


Prompt: An arithmetic sequence starts at a_1 = -10 with common difference 5. What is a_6? Return an integer.


Prompt:
Solve the following system of three linear equations for integer x, y, z:
  0x + (-2)y + (3)z = -6
  -4x + (-3)y + (-3)z = 42
  -5x + (-4)y + (-1)z = 47
Return only the integer value of x.


Prompt: An arithmetic sequence starts at a_1 = 4 with common difference 2. What is a_13? Return an integer.


Prompt: Count the number of monotone lattice paths from (0, 0) to (11, 11) that only step Right (r→r+1) or Up (c→c+1) by one unit, and that avoid all of the following forbidden grid cells: (2,7), (3,11), (4,10), (5,6), (8,3), (10,2). Both (0, 0) and (11, 11) are allowed. Return the integer count only.


Prompt: How many integers n with 1 ≤ n ≤ 90496 satisfy BOTH gcd(n, 21) = 1 AND gcd(n, 10) = 1? Return the integer count.


Prompt:
Solve the following system of three linear equations for integer x, y, z:
  -1x + (2)y + (4)z = -8
  4x + (-3)y + (3)z = -15
  4x + (-2)y + (-3)z = 5
Return only the integer value of x.


Prompt: How many ways are there to choose 4 elements from a set of 9?


Prompt:
Find the smallest non-negative integer x satisfying all of the following 12 congruences:
  x ≡ 6 (mod 9)
  x ≡ 23 (mod 37)
  x ≡ 9 (mod 29)
  x ≡ 1 (mod 7)
  x ≡ 6 (mod 8)
  x ≡ 4 (mod 43)
  x ≡ 5 (mod 11)
  x ≡ 21 (mod 23)
  x ≡ 15 (mod 19)
  x ≡ 6 (mod 25)
  x ≡ 5 (mod 47)
  x ≡ 22 (mod 41)
Return the integer x only.


Prompt: Compute 168 + 53. Give an integer.


Prompt: Find the smaller integer r with 1 ≤ r ≤ 2325 such that r^2 ≡ 4314 (mod 4651). Return the integer r only.


Prompt: Compute 70 * 76. Give an integer.


Prompt: Solve the discrete logarithm: find the integer x with 1 ≤ x ≤ 17400 such that 11^x ≡ 4124 (mod 17401). Return the integer x only.


Prompt: Compute 874 mod 14. Return the integer.


Prompt:
Solve the following system of three linear equations for integer x, y, z:
  4x + (-1)y + (-3)z = 31
  2x + (2)y + (-3)z = 12
  -4x + (-4)y + (4)z = -12
Return only the integer value of x.


Prompt:
Find the smallest non-negative integer x satisfying all of the following 12 congruences:
  x ≡ 11 (mod 13)
  x ≡ 6 (mod 7)
  x ≡ 3 (mod 11)
  x ≡ 0 (mod 4)
  x ≡ 3 (mod 17)
  x ≡ 7 (mod 9)
  x ≡ 0 (mod 5)
  x ≡ 14 (mod 47)
  x ≡ 19 (mod 37)
  x ≡ 27 (mod 29)
  x ≡ 13 (mod 43)
  x ≡ 30 (mod 31)
Return the integer x only.


Prompt: Find a non-negative integer x with 0 ≤ x < 19 such that 10*x + 19*y = 82 has an integer solution y. Return the integer x only.


Prompt: Compute 191 + 3. Give an integer.


Prompt: Solve for x: 2x + (24) = 78. Return the integer x.


Prompt:
Solve the following system of three linear equations for integer x, y, z:
  -1x + (2)y + (4)z = -9
  -4x + (-1)y + (-4)z = 52
  -1x + (1)y + (-4)z = 47
Return only the integer value of x.


Prompt: How many ways are there to choose 3 elements from a set of 4?


Prompt: Count the number of monotone lattice paths from (0, 0) to (10, 10) that only step Right (r→r+1) or Up (c→c+1) by one unit, and that avoid all of the following forbidden grid cells: (1,10), (3,1), (4,2), (4,9), (8,7), (9,9), (10,5), (10,6). Both (0, 0) and (10, 10) are allowed. Return the integer count only.


Prompt: Find the smaller integer r with 1 ≤ r ≤ 1218 such that r^2 ≡ 496 (mod 2437). Return the integer r only.


Prompt:
Find the smallest non-negative integer x satisfying all of the following 12 congruences:
  x ≡ 13 (mod 23)
  x ≡ 5 (mod 16)
  x ≡ 3 (mod 19)
  x ≡ 42 (mod 43)
  x ≡ 7 (mod 9)
  x ≡ 8 (mod 29)
  x ≡ 7 (mod 11)
  x ≡ 34 (mod 47)
  x ≡ 6 (mod 41)
  x ≡ 12 (mod 13)
  x ≡ 5 (mod 7)
  x ≡ 2 (mod 5)
Return the integer x only.


Prompt: Solve for x: 2x + (49) = 83. Return the integer x.


Prompt: Find the smaller integer r with 1 ≤ r ≤ 1146 such that r^2 ≡ 2012 (mod 2293). Return the integer r only.


Prompt: How many ways are there to choose 7 elements from a set of 10?


Prompt: Let σ(n) denote the sum of positive divisors of n (including 1 and n). Compute σ(82).


Prompt: Find the smaller integer r with 1 ≤ r ≤ 1724 such that r^2 ≡ 1551 (mod 3449). Return the integer r only.


Prompt: How many ways are there to choose 6 elements from a set of 8?


Prompt: Solve the discrete logarithm: find the integer x with 1 ≤ x ≤ 17476 such that 2^x ≡ 3754 (mod 17477). Return the integer x only.


Prompt: How many integers n with 1 ≤ n ≤ 76976 satisfy BOTH gcd(n, 55) = 1 AND gcd(n, 6) = 1? Return the integer count.


Prompt: Consider the Pell equation x^2 - 941*y^2 = 1, with x and y positive integers. Find the smallest positive integer y satisfying this equation. Return the integer y only.


Prompt: How many integers n with 1 ≤ n ≤ 22793 satisfy BOTH gcd(n, 6) = 1 AND gcd(n, 77) = 1? Return the integer count.


Prompt: Consider the Pell equation x^2 - 376*y^2 = 1, with x and y positive integers. Find the smallest positive integer y satisfying this equation. Return the integer y only.


Prompt:
Find the smallest non-negative integer x satisfying all of the following 12 congruences:
  x ≡ 23 (mod 37)
  x ≡ 5 (mod 11)
  x ≡ 4 (mod 13)
  x ≡ 0 (mod 4)
  x ≡ 0 (mod 7)
  x ≡ 8 (mod 17)
  x ≡ 1 (mod 27)
  x ≡ 39 (mod 43)
  x ≡ 29 (mod 47)
  x ≡ 2 (mod 25)
  x ≡ 11 (mod 19)
  x ≡ 9 (mod 41)
Return the integer x only.


Prompt:
Solve the following system of three linear equations for integer x, y, z:
  -3x + (-5)y + (3)z = -1
  1x + (3)y + (-1)z = -1
  0x + (-5)y + (-1)z = 12
Return only the integer value of x.


Prompt: How many integers n with 1 ≤ n ≤ 11998 satisfy BOTH gcd(n, 10) = 1 AND gcd(n, 77) = 1? Return the integer count.


Prompt:
Find the smallest non-negative integer x satisfying all of the following 12 congruences:
  x ≡ 34 (mod 37)
  x ≡ 1 (mod 7)
  x ≡ 21 (mod 27)
  x ≡ 5 (mod 29)
  x ≡ 11 (mod 17)
  x ≡ 10 (mod 19)
  x ≡ 6 (mod 8)
  x ≡ 19 (mod 43)
  x ≡ 2 (mod 5)
  x ≡ 7 (mod 31)
  x ≡ 6 (mod 11)
  x ≡ 3 (mod 47)
Return the integer x only.


Prompt: Find the multiplicative order of 1640 modulo 1901, i.e. the smallest positive integer k such that 1640^k ≡ 1 (mod 1901). Return the integer k only.


Prompt: Consider the Pell equation x^2 - 689*y^2 = 1, with x and y positive integers. Find the smallest positive integer y satisfying this equation. Return the integer y only.


Prompt: Maria saw the number 649 on a sign earlier today and the number 764 on a passing bus. After that, she received 11 stickers in the morning and 27 stickers in the afternoon. The signs and bus numbers are unrelated to her stickers. How many stickers does Maria have in total?


Prompt: Find the smaller integer r with 1 ≤ r ≤ 2258 such that r^2 ≡ 3213 (mod 4517). Return the integer r only.


Prompt: Solve the discrete logarithm: find the integer x with 1 ≤ x ≤ 7410 such that 2^x ≡ 3674 (mod 7411). Return the integer x only.


Prompt: How many integers n with 1 ≤ n ≤ 99024 satisfy BOTH gcd(n, 21) = 1 AND gcd(n, 10) = 1? Return the integer count.


Prompt: Compute 113 + 18. Give an integer.


Prompt:
Find the smallest non-negative integer x satisfying all of the following 12 congruences:
  x ≡ 8 (mod 41)
  x ≡ 19 (mod 27)
  x ≡ 40 (mod 43)
  x ≡ 2 (mod 7)
  x ≡ 16 (mod 19)
  x ≡ 5 (mod 25)
  x ≡ 7 (mod 29)
  x ≡ 8 (mod 32)
  x ≡ 9 (mod 37)
  x ≡ 5 (mod 11)
  x ≡ 31 (mod 47)
  x ≡ 13 (mod 23)
Return the integer x only.


Prompt: Count the number of monotone lattice paths from (0, 0) to (12, 12) that only step Right (r→r+1) or Up (c→c+1) by one unit, and that avoid all of the following forbidden grid cells: (1,10), (4,0), (4,7), (5,3), (5,8), (6,3), (8,11), (9,11), (11,7), (12,3). Both (0, 0) and (12, 12) are allowed. Return the integer count only.


Prompt: Find the smaller integer r with 1 ≤ r ≤ 1229 such that r^2 ≡ 1100 (mod 2459). Return the integer r only.


Prompt: Maria saw the number 129 on a sign earlier today and the number 103 on a passing bus. After that, she received 84 stickers in the morning and 67 stickers in the afternoon. The signs and bus numbers are unrelated to her stickers. How many stickers does Maria have in total?


Prompt: Solve for x: 10x + (26) = 376. Return the integer x.


Prompt: Solve for x: 11x + (40) = 326. Return the integer x.


Prompt: Maria saw the number 672 on a sign earlier today and the number 274 on a passing bus. After that, she received 57 stickers in the morning and 15 stickers in the afternoon. The signs and bus numbers are unrelated to her stickers. How many stickers does Maria have in total?


Prompt: A farmer has 118 apples. After 34 are eaten, the remaining apples are split equally into 2 bags (extras discarded). Each bag also receives 1 bonus apples (separately). How many apples are in one bag? Return an integer.


Prompt: An arithmetic sequence starts at a_1 = -4 with common difference 7. What is a_15? Return an integer.


Prompt:
Find the smallest non-negative integer x satisfying all of the following 12 congruences:
  x ≡ 14 (mod 47)
  x ≡ 17 (mod 27)
  x ≡ 3 (mod 4)
  x ≡ 17 (mod 43)
  x ≡ 5 (mod 17)
  x ≡ 17 (mod 29)
  x ≡ 15 (mod 23)
  x ≡ 2 (mod 5)
  x ≡ 33 (mod 41)
  x ≡ 8 (mod 11)
  x ≡ 7 (mod 13)
  x ≡ 34 (mod 37)
Return the integer x only.


Prompt: Maria saw the number 983 on a sign earlier today and the number 514 on a passing bus. After that, she received 26 stickers in the morning and 21 stickers in the afternoon. The signs and bus numbers are unrelated to her stickers. How many stickers does Maria have in total?


Prompt:
Solve the following system of three linear equations for integer x, y, z:
  -3x + (2)y + (-3)z = -7
  -5x + (-4)y + (-2)z = -69
  5x + (-3)y + (5)z = 14
Return only the integer value of x.


Prompt: An arithmetic sequence starts at a_1 = -3 with common difference 4. What is a_6? Return an integer.


Prompt:
Solve the following system of three linear equations for integer x, y, z:
  3x + (-2)y + (-4)z = 64
  -1x + (4)y + (-3)z = -22
  5x + (-5)y + (3)z = 62
Return only the integer value of x.