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• 2015 AMC 12B Problems/Problem 22
  ...nce the elements in a 2-cycle cannot differ by 1, 3, or 5 mod 6, they must differ by 2 or 4 mod 6, i.e. they must be of the same parity. But since we have th
  9 KB (1,623 words) - 18:48, 30 October 2022
• 2015 USAMO Problems
  ...e equivalent, but <math>\{1, 1, 2, 3\}</math> and <math>\{1, 2, 3\}</math> differ.)
  4 KB (629 words) - 13:49, 22 November 2023
• Algebraic number theory
  ...that no two of these irreducibles are <b>associates</b>; i.e. they do not differ only by [[unit (ring theory)|units]]. Fortunately, it is easy to verify tha
  10 KB (1,646 words) - 15:04, 28 May 2020
• 2015 AMC 8 Problems/Problem 11
  ...> consonants), <math>20</math> choices for the third letter (since it must differ from the second letter), and <math>10</math> choices for the digit. This l
  2 KB (319 words) - 23:58, 16 May 2023
• 2015 AMC 8 Problems/Problem 10
  ...first two, and <math>7</math> choices for the fourth number, since it must differ from all three. This means there are <math>9 \times 9 \times 8 \times 7=\b
  1 KB (165 words) - 11:22, 23 November 2023
• 2016 AMC 12A Problems/Problem 25
  ...this process continues until the last two numbers that remain on the board differ by at least 2. Let <math>f(k)</math> be the smallest positive integer not w ...ill show the hundreds place at the end. In order for the hundreds place to differ by 2, the difference between two perfect squares needs to be at least <math
  8 KB (1,224 words) - 18:28, 16 November 2022
• 1953 AHSME Problems/Problem 11
  ...les. It is <math>10</math> feet wide. The circumference of the two circles differ by about:
  814 bytes (124 words) - 12:23, 22 April 2020
• Mock AIME 3 2010 Problems
  ...ith integer side lengths almost isosceles if its two shortest side lengths differ by 1. The
  14 KB (2,904 words) - 18:24, 16 May 2017
• 2017 AMC 12A Problems/Problem 16
  ...hts. Because the bases of these two triangles (that have the same heights) differ by a factor of 2, the area of <math>\Delta CBP</math> must be twice that of
  13 KB (1,982 words) - 17:12, 20 December 2022
• 2020 AMC 12B Problems
  ...in which the factors are listed matters (that is, two representations that differ only in the order of the factors are counted as distinct). For example, the
  16 KB (2,417 words) - 01:03, 28 April 2022
• 2018 AIME II Problems/Problem 15
  Because <math>f(n)</math> and <math>f(n+1)</math> can differ by at most 3 for <math>n=0,1,2,3,4,5</math>, <math>f</math> can decrease at
  9 KB (1,607 words) - 10:27, 4 February 2022
• 2008 iTest Problems/Problem 87
  ...rom the alphabet <math>\{0,1,2,3,4,5,6\}</math> if neighboring digits must differ by exactly <math>2</math>. ...numbers" are 1 and 5, and the middle number is 3. Since neighboring digits differ by exactly 2, the outer numbers and the middle number must alternate. Denot
  3 KB (451 words) - 20:25, 23 November 2018
• 2020 AMC 10B Problems
  ...in which the factors are listed matters (that is, two representations that differ only in the order of the factors are counted as distinct). For example, the
  16 KB (2,496 words) - 20:09, 19 May 2024
• 2019 AIME I Problems/Problem 12
  The arguments of the two complex numbers differ by <math>90^\circ</math> if the ratio of the numbers is a pure imaginary nu
  8 KB (1,534 words) - 22:17, 28 December 2023
• What is the definition of Pure Mathematics?
  Two primes that differ by exactly 2 are known as twin primes. The following are the first few pai
  35 KB (5,882 words) - 18:08, 28 June 2021
• 1975 AHSME Problems/Problem 22
  ...math> and <math>q</math> and <math>p=q+1</math>. The only two primes which differ by <math>1</math> are <math>2,3</math> so <math>p=3</math> and <math>q=2</m
  1 KB (226 words) - 17:48, 19 January 2021
• 2020 AMC 10B Problems/Problem 25
  ...in which the factors are listed matters (that is, two representations that differ only in the order of the factors are counted as distinct). For example, the
  16 KB (2,562 words) - 17:41, 25 May 2024
• 2020 USOJMO Problems/Problem 3
  ...ordinates, and similarly call it x-oriented or y-oriented if the endpoints differ in x- or y-coordinates, respectively.
  5 KB (769 words) - 19:14, 6 October 2023
• 2022 AIME II Problems
  ...e order. A line segment is drawn between every pair of points whose labels differ by a prime number. Find the number of triangles formed whose vertices are a
  8 KB (1,397 words) - 09:18, 15 August 2022
• 2021 Fall AMC 10B Problems
  ...y <math>3</math> degrees, at which time the temperatures in the two cities differ by <math>2</math> degrees. What is the product of all possible values of <m
  16 KB (2,450 words) - 09:34, 9 June 2024

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