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• Prime Number Theorem
  The '''Prime Number Theorem''' (PNT) is one of the most celebrated results in [[analytic number theory]]. Indeed, it is
  10 KB (1,729 words) - 19:52, 21 October 2023
• Infinite
  ...n]] <math>f:S\to\mathbb{Z}</math>. If this is not the case, <math>S</math> is said to be [[finite]]. In simplified language, a set is infinite if it doesn't end, i.e. you can always find another element that y
  1 KB (186 words) - 23:19, 16 August 2013
• Isosceles trapezoid
  ...isosceles trapezoid''' is a geometric figure that lies in a [[plane]]. It is a specific type of [[trapezoid]] in which the legs have the same length. I * the segment joining the midpoints of the bases is perpendicular to the bases
  577 bytes (81 words) - 10:33, 18 April 2019
• Mock AMC
  A '''Mock AMC''' is a contest intended to mimic an actual [[AMC]] (American Mathematics Competi ...popular in the months leading up to the actual [[AMC]] competition. There is no guarantee that community members will make Mock AMCs in any given year,
  51 KB (6,175 words) - 20:58, 6 December 2023
• Mock AIME
  A '''Mock AIME''' is a contest that is intended to mimic the [[AIME]] competition. (In more recent years, recurrin ...Y2QwOTc3NWZiYjY0LnBkZg==&rn=TWlsZG9yZiBNb2NrIEFJTUUucGRm Mildorf Mock AIME 3]
  8 KB (933 words) - 22:41, 23 May 2024
• Permutation
  A '''permutation''' of a [[set]] of <math>r</math> objects is any rearrangement (linear ordering) of the <math>r</math> objects. There a ...of [[infinite]] sets. In this case, a permutation of a set <math>S</math> is simply a [[bijection]] between <math>S</math> and itself.
  3 KB (422 words) - 11:01, 25 December 2020
• Riemann zeta function
  The '''Riemann zeta function''' is a function very important in [[number theory]]. In particular, the [[Riemann Hypothesis]] is a conjecture
  9 KB (1,547 words) - 03:04, 13 January 2021
• Mock USAMO
  ...hen a mock USAMO is run on [[AoPS]]/[[MathLinks]], a very wide time window is often allowed to take the mock USAMO. ** [http://www.artofproblemsolving.com/blog/2712 Mock USAMO 3 2006]
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• Modular arithmetic/Introduction
  ...of arithmetic that involves only [[integers]]. This goal of this article is to explain the basics of modular arithmetic while presenting a progression <math>1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 0, \ldots </math>
  15 KB (2,396 words) - 20:24, 21 February 2024
• Perfect square
  An [[integer]] <math>n</math> is said to be a '''perfect square''' if there is an integer <math>m</math> so that <math>m^2=n</math>. The first few perfect ...of the first <math>n</math> square numbers (starting with <math>1</math>) is <math>\frac{n(n+1)(2n+1)}{6}</math>
  954 bytes (155 words) - 01:14, 29 November 2023
• Uncountable
  ...or [[countably infinite]]. The most common example of an uncountable set is the set of [[real number]]s <math>\mathbb{R}</math>. == Proof that <math>\mathbb{R}</math> is uncountable ==
  2 KB (403 words) - 20:53, 13 October 2019
• Modular arithmetic/Intermediate
  ...quiv b</math> (mod <math>n</math>), if the difference <math>{a - b}</math> is divisible by <math>n</math>. ...<math>n</math>, the relation <math>a \equiv b</math> (mod <math>n</math>) is an [[equivalence relation]] on the set of integers. This relation gives ri
  14 KB (2,317 words) - 19:01, 29 October 2021
• Right triangle
  A '''right triangle''' is any [[triangle]] with an angle of 90 degrees (that is, a [[right angle]]). A = (0, 3);
  3 KB (499 words) - 23:41, 11 June 2022
• 2006 AIME I Problems
  ..., \angle B </math> is a right angle, diagonal <math> \overline{AC} </math> is perpendicular to <math> \overline{CD}, AB=18, BC=21, </math> and <math> CD Let set <math> \mathcal{A} </math> be a 90-element subset of <math> \{1,2,3,\ldots,100\}, </math> and let <math> S </math> be the sum of the elements o
  7 KB (1,173 words) - 03:31, 4 January 2023
• 2006 AIME I Problems/Problem 15
  ...n that a sequence satisfies <math> x_0=0 </math> and <math> |x_k|=|x_{k-1}+3| </math> for all integers <math> k\ge 1, </math> find the minimum possible Suppose <math>b_{i} = \frac {x_{i}}3</math>.
  6 KB (910 words) - 19:31, 24 October 2023
• 2006 AIME I Problems/Problem 14
  ...notation <math> \lfloor x\rfloor </math> denotes the greatest integer that is less than or equal to <math> x. </math>) currentprojection = perspective(1,-10,3.3);
  6 KB (980 words) - 21:45, 31 March 2020
• 2006 AIME I Problems/Problem 13
  ...atest integer <math> n </math> less than 1000 such that <math> S_n </math> is a [[perfect square]]. ...h>k</math> is odd, then <math>n+1</math> is even, hence <math>k+n-1</math> is odd, and <math>S_n</math> cannot be a perfect square. Hence <math>k</math>
  10 KB (1,702 words) - 00:45, 16 November 2023
• 2006 AIME I Problems/Problem 11
  ...h> k </math> for each [[integer]] <math> k, 1 \le k \le 8. </math> A tower is to be built using all 8 cubes according to the rules: ...s than can be constructed. What is the [[remainder]] when <math> T </math> is divided by 1000?
  3 KB (436 words) - 05:40, 4 November 2022
• 2006 AIME I Problems/Problem 10
  ...d <math> c </math> are positive integers whose [[greatest common divisor]] is 1. Find <math> a^2+b^2+c^2. </math> int[] array={3,3,2};
  4 KB (731 words) - 17:59, 4 January 2022
• 2006 AIME I Problems/Problem 9
  The [[sequence]] <math> a_1, a_2, \ldots </math> is [[geometric sequence|geometric]] with <math> a_1=a </math> and common [[rat ...<math>a, r</math> [[positive integer]]s. <math>a^{12}r^{66}=8^{2006} = (2^3)^{2006} = (2^6)^{1003}</math> so <math>a^{2}r^{11}=2^{1003}</math>.
  4 KB (651 words) - 18:27, 22 May 2021

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