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Twin Prime Conjecture
The '''Twin Prime Conjecture''' is a [[conjecture]] (i.e., not a [[theorem]]) that states that there are [[inf One possible strategy to prove the infinitude of twin primes is an idea adopted from the proof of [[Dirichlet's Theorem]]. If one can show

2 KB (308 words) - 02:27, 1 May 2024
Quadratic residues
...</math> if there is some integer <math>n</math> so that <math>n^2-a</math> is [[divisibility | divisible]] by <math>m</math>. ...modulo\ }\ p, \\ -1 & \mathrm{if }\ p\nmid a\ \mathrm{ and }\ a\ \mathrm{\ is\ a\ quadratic\ nonresidue\ modulo\ }\ p. \end{cases}</math>

5 KB (778 words) - 13:10, 29 November 2017
Power of a Point Theorem
The '''Power of a Point Theorem''' is a relationship that holds between the lengths of the [[line segment]]s form # One of the lines is [[tangent line|tangent]] to the circle while the other is a [[secant line|secant]] (middle figure). In this case, we have <math> AB^2

5 KB (828 words) - 23:10, 25 June 2024
Collatz Problem
...th>\{n,f(n),f(f(n)),f(f(f(n))),\ldots\}</math> contains 1. This conjecture is still open. Some people have described it as the easiest unsolved problem i ...6m+4\over 2}=3m+2</cmath> we can then observe that; only if <math>m</math> is even will another division by 2 be possible.

1 KB (231 words) - 19:45, 24 February 2020
Algebraic number
...[27]{19}}{\sqrt[3]{4}+\sqrt[7]{97}}</math>. A number that is not algebraic is called a [[transcendental number]], such as <math>e</math> or <math>\pi</ma ...mbers is large, there are only [[countable|countably]] many of them. That is, the algebraic numbers have the same [[cardinality]] as the [[natural numbe

1,006 bytes (151 words) - 21:56, 22 April 2022
International Mathematical Olympiad
The '''International Mathematical Olympiad''' is the pinnacle of all high school [[mathematics competition]]s and the oldest ...eakdown=Problem 1/4: 6.5 Problem 2/5: 7.5-8 Problem 3/6: 9.5 Problem SL1-2: 5.5-7 Problem SL3-4: 7-8 <

3 KB (490 words) - 03:32, 23 July 2023
AoPS Wiki talk:AoPS Community Awards
...is very very far from complete, but there's no way I can know who everyone is or track down every major award, so I'll leave most of the rest for the com ...it and simply link to that page from this one, but I also feel like there is a long list of accomplishments that would be more noteable that we aren't a

4 KB (611 words) - 07:36, 14 April 2012
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]

2 KB (205 words) - 19:56, 4 March 2020
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

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