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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
  2 KB (308 words) - 02:27, 1 May 2024
• 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
• 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
• 2010 AIME II Problems/Problem 3
  ...al, there are <math>20-n</math> pairs of integers <math>(a, b)</math> that differ by <math>n</math> because we can let <math>b</math> be any integer from <ma
  2 KB (303 words) - 15:17, 12 May 2020
• 2010 USAMO Problems/Problem 3
  Now, when the indices differ by <math>1</math> we have ensured equality (and
  11 KB (1,889 words) - 13:45, 4 July 2013
• 2011 AMC 10B Problems/Problem 25
  ...math>). All additional triangles will differ by one as the solutions above differ by one so this process can be repeated indefinitely until the side lengths
  4 KB (620 words) - 03:15, 3 November 2022
• 2011 AMC 10A Problems/Problem 19
  ...9,784,841,900,961</cmath>We see that <math>484</math> and <math>784</math> differ by <math>300</math>, and we can confirm that <math>484</math> is the correc
  3 KB (545 words) - 20:54, 21 August 2023
• 2003 AMC 8 Problems
  ...ookies, and all cookies have the same thickness. The shapes of the cookies differ, as shown.
  16 KB (2,236 words) - 12:02, 19 February 2024
• 2003 AMC 8 Problems/Problem 8
  ...ookies, and all cookies have the same thickness. The shapes of the cookies differ, as shown.
  2 KB (320 words) - 00:47, 5 July 2013
• 2003 AMC 8 Problems/Problem 9
  ...ookies, and all cookies have the same thickness. The shapes of the cookies differ, as shown.
  2 KB (304 words) - 19:14, 28 August 2016
• 2003 AMC 8 Problems/Problem 10
  ...ookies, and all cookies have the same thickness. The shapes of the cookies differ, as shown.
  2 KB (245 words) - 00:47, 5 July 2013
• 2012 AMC 10A Problems/Problem 20
  ...o choose from). However, we must subtract the ways where two white squares differ by a rotation of 90 degrees about the middle of the square. There are a tot ...ion of 90 degrees and minus when there are 3 squares such that two of them differ by rotation of 90 and 1 of them differs by rotation of 180, because of the
  6 KB (1,001 words) - 22:19, 29 December 2023
• 1953 AHSME Problems
  ...les. It is <math>10</math> feet wide. The circumference of the two circles differ by about:
  21 KB (3,123 words) - 14:24, 20 February 2020
• 1989 AHSME Problems/Problem 22
  ...th> shapes (circle, hexagon, square, triangle). How many blocks in the set differ from the 'plastic medium red circle' in exactly <math>2</math> ways? (The ' ...he 'plastic medium red circle' in one of its qualities <math>(1)</math> or differ from it in <math>k</math> different ways <math>(kx)</math>. Choosing the ma
  3 KB (507 words) - 20:48, 6 December 2021
• 1996 USAMO Problems/Problem 2
  ...ses in such a way that the maximum and minimum sum belonging to each class differ by no more than a factor of 2.''' Using the previous notation, we first pro
  4 KB (823 words) - 11:40, 29 September 2019
• 2014 AIME II Problems/Problem 10
  ...degrees apart from <math>3 \theta_z</math> , so <math>\theta_w</math> must differ from <math>\theta_z</math> by some multiple of 120 degrees.
  6 KB (1,045 words) - 13:08, 21 January 2024
• 1995 USAMO Problems/Problem 4
  ...1,\ldots, x-d)</math> from <math>kQ(x)</math>; hence <math>q_x</math> must differ by a multiple of <math>\frac{x(x-1)\cdots (x-d)}{kd!(d-1)!\cdots 1!}</math>
  3 KB (502 words) - 15:27, 11 May 2018
• 1971 IMO Problems/Problem 5
  2. Two vector sums are at unit distance from one another if and only if they differ in presence of exactly one summand (i.e. one and only one coefficient <math
  4 KB (749 words) - 14:09, 29 January 2021
• 1962 AHSME Problems/Problem 36
  ...<math>x-8</math> and <math>x-10</math> are both powers of two; since they differ by two, it must be the case that <math>(x-8,x-10) = (4,2)</math> or <math>(
  729 bytes (120 words) - 15:01, 15 June 2018
• 2015 USAMO Problems/Problem 6
  ...e equivalent, but <math>\{1, 1, 2, 3\}</math> and <math>\{1, 2, 3\}</math> differ.)
  3 KB (560 words) - 21:08, 15 December 2018
• 2014 AMC 12B Problems
  ...consecutively on the circle that sum to <math>n</math>. Arrangements that differ only by a rotation or a reflection are considered the same. How many diffe
  13 KB (2,066 words) - 14:08, 1 November 2022
• 2014 AMC 10B Problems
  ...consecutively on the circle that sum to <math>n</math>. Arrangements that differ only by a rotation or a reflection are considered the same. How many differ
  13 KB (2,011 words) - 21:54, 8 November 2022
• 2014 AMC 10B Problems/Problem 24
  ...consecutively on the circle that sum to <math>n</math>. Arrangements that differ only by a rotation or a reflection are considered the same. How many differ
  7 KB (1,133 words) - 12:46, 12 March 2022
• 2014 AMC 12B Problems/Problem 10
  ...5</math>, so <math>a</math> and <math>c</math> must either be the equal or differ by <math>5</math>. We can quickly conclude that the former is impossible, s
  2 KB (321 words) - 19:46, 17 January 2021
• 2014 AMC 12B Problems/Problem 18
  ...consecutively on the circle that sum to <math>n</math>. Arrangements that differ only by a rotation or a reflection are considered the same. How many differ
  2 KB (331 words) - 04:43, 12 January 2021
• 1992 AHSME Problems/Problem 14
  The equations differ at <math>x=-2</math>. The graph of <math>I</math> would contain the point <
  938 bytes (164 words) - 22:45, 18 January 2018
• 1970 AHSME Problems/Problem 14
  ...th> and <math>q</math> are positive numbers. If the roots of this equation differ by 1, then <math>p</math> equals
  783 bytes (128 words) - 01:30, 24 February 2023
• 1970 AHSME Problems
  ...th> and <math>q</math> are positive numbers. If the roots of this equation differ by <math>1</math>, then <math>p</math> equals
  15 KB (2,366 words) - 07:52, 26 December 2023
• 2013 UNCO Math Contest II Problems
  ...at most six digits? (Consider two nonterminating decimals distinct if they differ in any digit. Nonterminating means that the digits are not eventually all z
  11 KB (1,648 words) - 09:55, 20 December 2021
• 2013 UNCO Math Contest II Problems/Problem 9
  ...at most six digits? (Consider two nonterminating decimals distinct if they differ in any digit. Nonterminating means that the digits are not eventually all z
  1 KB (205 words) - 03:29, 13 January 2019
• 2009 UNCO Math Contest II Problems
  elements and such that no two elements of <math>A</math> differ by <math>1</math> when
  5 KB (753 words) - 20:35, 8 February 2024
• 2009 UNCO Math Contest II Problems/Problem 10
  elements and such that no two elements of <math>A</math> differ by <math>1</math> when
  666 bytes (98 words) - 01:59, 13 January 2019
• 2016 AMC 12A Problems
  ...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
  15 KB (2,348 words) - 17:20, 19 January 2024
• 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 (2,497 words) - 21:14, 12 November 2023
• 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 (2,560 words) - 20:26, 11 November 2023
• 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) - 00:13, 12 November 2023
• 1977 IMO Problems
  ...ndecomposable in <math>V_n</math> in more than one way. (Expressions which differ only in order of the elements of <math>V_n</math> will be considered the sa
  3 KB (466 words) - 16:54, 29 January 2021
• 1977 IMO Problems/Problem 3
  ...ndecomposable in <math>V_n</math> in more than one way. (Expressions which differ only in order of the elements of <math>V_n</math> will be considered the sa
  2 KB (368 words) - 16:43, 29 January 2021
• 2021 AIME II Problems/Problem 11
  ...larly, if they differ by 3, there will be only 1 possible set, and if they differ by 1, 3 possible sets. ...so the condition is met. Now, this means that the multiple of 6 and 7 must differ by 1.
  15 KB (2,211 words) - 10:59, 4 February 2024
• Jadhav Triads
  ...square roots of the numbers which are also the product of numbers which '''differ by 2.''' It is found that the square root of the product may '''differ to maximum of 0.3 to minimum of 0.1''' from actual middle number, but this
  1 KB (188 words) - 10:34, 17 April 2021
• 2002 AMC 10P Problems/Problem 15
  ...ots \; , 20 \}</math> of size <math>n</math> must contain two numbers that differ by 8? ...; \{ 12, 20 \}</math> in <math>\{ 1, 2, 3, \; \dots \; , 20 \}</math> that differ by 8. If we take <math>n = 12</math>, it could be that we selected one elem
  900 bytes (122 words) - 11:24, 9 March 2021
• 2022 AIME II Problems/Problem 5
  ...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
  3 KB (481 words) - 11:08, 28 January 2024
• 2022 AIME II Problems/Problem 8
  ...nd <math>c</math>, since they make either <math>a</math> or <math>b</math> differ by at least 1.
  13 KB (2,136 words) - 22:39, 31 December 2023
• 2021 IMO Problems/Problem 1
  ...<math>\sqrt{1 + n} - 1</math> and <math>\sqrt{1 + \frac{n}{2}} + 1</math> differ by at least <math>1</math>, then we can guarantee that there is an integer
  5 KB (955 words) - 07:32, 13 April 2024
• 2021 Fall AMC 12B Problems/Problem 3
  ...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
  2 KB (353 words) - 13:51, 30 December 2022
• 2021 Fall AMC 12B 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
  14 KB (2,191 words) - 19:57, 12 November 2023
• Coterminal angles
  Angles are said to be coterminal if their angle measures differ by a multiple of <math>360^{\circ} = 2\pi \, \mathrm{rad}</math>. Cotermina
  312 bytes (43 words) - 13:26, 12 March 2022
• 2022 AMC 10A Problems/Problem 20
  ...has a perfect square factor and at least one other factor and those should differ by <math>2</math>.
  4 KB (583 words) - 22:29, 6 October 2023
• 2022 AMC 10A Problems/Problem 13
  ...ath> and <math>D</math> are the same, and their <math>x</math>-coordinates differ by <math>10</math>, the distance between them is <math>10</math>. Our answe
  7 KB (1,157 words) - 20:21, 23 January 2024
• Therapy Dogs
  ...hey are also capable of becoming Emotional Service Animals (note that ESAs differ from service dogs when it comes to legal protections).
  3 KB (370 words) - 15:48, 27 November 2022
• 2023 AIME I Problems/Problem 1
  ...plicity purposes, we consider two arrangements different even if they only differ by rotations or reflections. In this way, there are <math>14!</math> arrang
  11 KB (1,803 words) - 17:17, 12 January 2024
• 2016 Mathcounts State Sprint Problems
  all positive integers. If the range of f contains two numbers that differ by <math>20</math>,
  11 KB (1,672 words) - 21:18, 12 March 2023
• 2023 AMC 10A Problems
  ...differ by <math>20</math> and another pair of complementary divisors that differ by <math>23</math>. What is the sum of the digits of <math>N</math>?
  16 KB (2,411 words) - 15:11, 10 February 2024
• 1997 IMO Problems/Problem 6
  ...<math>2</math> with nonnegative integer exponents. Representations which differ only in the ordering of their summands are considered to be the same. For
  709 bytes (103 words) - 01:02, 17 November 2023
• 2023 AMC 10A Problems/Problem 23
  ...differ by <math>20</math> and another pair of complementary divisors that differ by <math>23</math>. What is the sum of the digits of <math>N</math>? Since we are given that some pairs of divisors differ by 20 and 23 and we can let the pair be <math>(x-10)</math> and <math>(x+10
  8 KB (1,344 words) - 01:16, 3 March 2024