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• Associative property
  ...are not equal for all choices of <math>a, b, c</math> (in particular, they differ whenever <math>c \neq 0</math>).
  1 KB (222 words) - 16:09, 15 August 2006
• Chinese Remainder Theorem
  ...orem. The converse follows because <math>a</math> and <math>b</math> must differ by a multiple of <math>m</math> and <math>n</math>, and <math>\mbox{lcm}(m, ...r]]. Moreover, in the case when the problem is solvable, any two solutions differ by some [[common multiple]] of <math>m_1,\ldots,m_n</math>.'' (the extended
  6 KB (1,022 words) - 14:57, 6 May 2023
• 2003 AMC 12A Problems/Problem 1
  ...e see that each of the <math>n</math>th term in the series of even numbers differ by <math>1</math>. For example, take series <math>O</math> and <math>E_1</m
  3 KB (436 words) - 20:31, 28 December 2021
• 2002 IMO Shortlist Problems/A2
  Thus for any <math>n </math>, we have two <math>a_i </math> that differ by more than <math> \frac{(n-1)^2}{n(n+1)} </math>. But this becomes arbi
  3 KB (448 words) - 17:58, 20 August 2008
• 2007 AIME I Problems/Problem 4
  ...linear, <math>a(t)</math>, <math>b(t) </math>, and <math>c(t) </math> must differ by a multiple of <math>\pi </math>. Note that <math> a(t) - b(t) = \frac{t
  1 KB (228 words) - 18:46, 11 March 2021
• 2004 IMO Shortlist Problems/A3
  ...laystyle n </math>. We also note that if <math> \displaystyle x,y </math> differ by an integer, then <math> \displaystyle t(x) = t(y) </math>.
  6 KB (958 words) - 22:15, 9 June 2007
• Sum and difference of powers
  An amazing thing happens when <math>x</math> and <math>y</math> differ by <math>1</math>, say, <math>x = y+1</math>. Then <math>x-y = 1</math> and
  3 KB (450 words) - 17:47, 26 March 2024
• 2006 AIME II Problems/Problem 8
  ...rotation and reflection. Thus, to make two triangles distinct, they must differ either in their center triangle or in the collection of colors which make u
  4 KB (695 words) - 10:37, 4 November 2023
• 1990 USAMO Problems
  ...g of six digits (from 0 through 9). The state requires that any two plates differ in at least two places. (Thus the plates <math>\boxed{027592}</math> and <m
  3 KB (386 words) - 20:47, 3 July 2013
• 1990 USAMO Problems/Problem 1
  ...g of six digits (from 0 through 9). The state requires that any two plates differ in at least two places. (Thus the plates <math>\boxed{027592}</math> and <m ...plates which agree on the first <math>n-1</math> digits; these plates thus differ only on one digit, the last one.
  2 KB (292 words) - 14:28, 20 November 2019
• 2007 AMC 10A Problems/Problem 23
  ...nteger]]s, with <math>m \ge n</math>, have the property that their squares differ by <math>96</math>?
  2 KB (352 words) - 14:20, 3 July 2023
• 2007 AMC 10A Problems
  ...integers, with <math>m \ge n</math>, have the property that their squares differ by <math>96</math>?
  13 KB (2,058 words) - 17:54, 29 March 2024
• 2008 AMC 12B Problems/Problem 21
  In other words, the two chosen <math>x</math>-coordinates must differ by no more than <math>\sqrt{3}</math>. To find this probability, we divide
  6 KB (1,008 words) - 11:46, 24 December 2020
• 2008 AIME I Problems/Problem 4
  ...cutive odd numbers, we note that <math>y</math> and <math>x+42</math> must differ by an even number. We can use casework with the even numbers, starting with
  4 KB (732 words) - 22:17, 28 November 2023
• KGS math club
  ...mmunication channel, how can they (1) check whether their length-two lists differ; and if they do, (2) let each other know who the murderer is? They must not
  22 KB (3,358 words) - 15:17, 18 July 2017
• 2008 iTest Problems
  ...rom the alphabet <math>\{0,1,2,3,4,5,6\}</math> if neighboring digits must differ by exactly <math>2</math>.
  71 KB (11,749 words) - 01:31, 2 November 2023
• 2002 AMC 12A Problems/Problem 13
  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>?
  1 KB (189 words) - 20:43, 25 August 2022
• 2000 AMC 10 Problems/Problem 20
  ...uppose that some two of <math>A</math>, <math>M</math>, and <math>C</math> differ by at least <math>2</math>. Then this triple <math>(A,M,C)</math> is not o
  2 KB (447 words) - 18:12, 22 April 2023
• Simple harmonic motion
  ...e mathematically represented by the following cosine (or sine, which would differ by a phase constant) function:
  926 bytes (145 words) - 06:07, 23 February 2023
• Change of base formula
  ...he functions <math>f(x) = \log_a x</math> and <math>g(x) = \log_b x</math> differ by a constant factor, <math>f(x) = (\log_a b) g(x)</math> for all <math>x >
  2 KB (412 words) - 15:32, 22 February 2024

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