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• Mathematics competitions
  Math competitions differ widely in difficulty and content. Most test a broader range of mathematics
  698 bytes (88 words) - 14:36, 24 January 2024
• Prime number
  Two primes that differ by exactly 2 are known as [[twin primes]]. The following are the first few
  6 KB (985 words) - 12:38, 25 February 2024
• Mathematical Kangaroo
  ...bsites have released their problems from past years. The various versions differ from each other in terms of names and grammar usage. Most problems remain
  6 KB (936 words) - 15:38, 22 February 2024
• Twin Prime Conjecture
  ...re [[infinite]]ly many pairs of [[twin prime]]s, i.e. pairs of primes that differ by <math>2</math>. This version stated that there are infinitely many pairs of primes that differ by a finite number. The number Yitang chose was 7,000,000. Terence Tao and
  7 KB (1,193 words) - 14:18, 7 January 2022
• Partition of a rectangle into squares problem
  ...iplication by <math>q</math>. So, we may assume that all these coordinates differ from integers by, at most, <math>\frac 15</math>. Now let <math>a</math> an
  2 KB (333 words) - 13:50, 26 June 2006
• Modular arithmetic/Intermediate
  ...d <math>b</math> from the same set, then <math>a</math> and <math>b</math> differ by a multiple of <math>3</math>, and therefore <math>a \equiv b \pmod{3}.</
  14 KB (2,317 words) - 19:01, 29 October 2021
• Limit
  If the left hand and right hand limits at a certain point differ, than the limit does not exist at that point. For example, if we consider t
  7 KB (1,325 words) - 13:51, 1 June 2015
• 2002 AMC 12A Problems
  Two different positive numbers <math>a</math> and <math>b</math> each differ from their reciprocals by <math>1</math>. What is <math>a+b</math>?
  12 KB (1,792 words) - 13:06, 19 February 2020
• 2006 AMC 12A Problems/Problem 24
  ...ath> cannot combine and simplify, as their exponent of <math>x</math> will differ. Therefore, we simply add the number of terms produced from each addend. By
  8 KB (1,332 words) - 17:37, 17 September 2023
• 2005 AIME II Problems/Problem 13
  ...\; n_1-24 \mid 10.</cmath>We look for two divisors of <math>10</math> that differ by <math>7</math>; we find that <math>\{2, -5\}</math> and <math>\{5, -2\}<
  4 KB (642 words) - 14:55, 12 August 2019
• 2019 AIME I Problems/Problem 2
  ...e <math>P</math> is the probability that <math>B</math> and <math>J</math> differ by <math>1</math> (no zero, because the two numbers are distinct). There ar ...h>, the numbers differ by less than 2, so the probability that the numbers differ by at least 2 is <math>1-\tfrac{19}{190}=\tfrac9{10}</math>. Then <math>B-J
  5 KB (830 words) - 22:15, 28 December 2023
• 1989 AIME Problems
  ...}_{},\ldots,1989\}</math> such that no two members of <math>S^{}_{}</math> differ by <math>4^{}_{}</math> or <math>7^{}_{}</math>. What is the largest number
  7 KB (1,045 words) - 20:47, 14 December 2023
• 2003 AIME I Problems
  ...t three terms form a geometric progression, and the first and fourth terms differ by <math>30.</math> Find the sum of the four terms.
  6 KB (965 words) - 16:36, 8 September 2019
• 2003 AIME II Problems
  Two positive integers differ by <math>60.</math> The sum of their square roots is the square root of an
  7 KB (1,127 words) - 09:02, 11 July 2023
• 1989 AIME Problems/Problem 13
  ...th>\{1,2,3,\ldots,1989\}</math> such that no two members of <math>S</math> differ by <math>4</math> or <math>7</math>. What is the largest number of [[elemen
  2 KB (274 words) - 04:07, 17 December 2023
• 1993 AIME Problems/Problem 4
  ...does not work, because if <math>c-d = 2</math>, then <math>a+b</math> must differ by 2 as well, but an odd number <math>93</math> can only result from two nu
  8 KB (1,343 words) - 16:27, 19 December 2023
• 2000 AIME I Problems/Problem 6
  ...ot easier since now we just have to find all pairs <math>(a,b)</math> that differ by 2.
  6 KB (966 words) - 21:48, 29 January 2024
• 2003 AIME I Problems/Problem 8
  ...ree terms form a [[geometric progression]], and the first and fourth terms differ by <math>30</math>. Find the sum of the four terms. Since the first and fourth terms differ by <math>30</math>, we have that <math>\frac{(a + 2d)^2}{a + d} - a = 30</m
  5 KB (921 words) - 23:21, 22 January 2023
• 2003 AIME II Problems/Problem 10
  Two positive integers differ by <math>60</math>. The sum of their square roots is the square root of an
  1 KB (218 words) - 14:14, 25 June 2021
• 2000 AMC 12 Problems/Problem 8
  We know that 1 and 5 differ by 4, 5 and 13 differ by 8, and 13 and 25 differ by 12. Hence the differences are 4, 8, and 12, resp. And the differences of
  7 KB (988 words) - 15:14, 10 April 2024

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