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• Fermat's Little Theorem
  ...] (which students should study more at the introductory level if they have a hard time following the rest of this article). This theorem is credited to ...}</math> is not [[divisibility|divisible]] by <math>{p}</math>, then <math>a^{p-1}\equiv 1 \pmod {p}</math>.
  16 KB (2,658 words) - 16:02, 8 May 2024
• Euler's Totient Theorem
  '''Euler's Totient Theorem''' is a theorem closely related to his [[totient function]]. ...tively prime]] to <math>a</math>, then <math>{a}^{\phi (m)}\equiv 1 \pmod {m}</math>.
  3 KB (542 words) - 17:45, 21 March 2023
• Geometric inequality
  A '''geometric inequality''' is an [[inequality]] involving various measures ...level geometry problems. It also provides the basis for the definition of a [[metric space]] in [[analysis]].
  7 KB (1,296 words) - 14:22, 22 October 2023
• Ptolemy's theorem
  ...orem''' gives a relationship between the side lengths and the diagonals of a [[cyclic quadrilateral]]; it is the [[equality condition | equality case]] Given a [[cyclic quadrilateral]] <math>ABCD</math> with side lengths <math>{a},{b},{c},{d}</math> and [[diagonal]]s <math>{e},{f}</math>:
  7 KB (1,198 words) - 20:39, 9 March 2024
• Euler's totient function
  '''Euler's totient function''' <math>\phi(n)</math> applied to a [[positive integer]] <math>n</math> is defined to be the number of positive ...ere the <math>p_i </math> are distinct [[prime number]]s. Now, we can use a [[PIE]] argument to count the number of numbers less than or equal to <mat
  5 KB (898 words) - 19:12, 28 January 2024
• Real number
  A '''real number''' is a number that falls on the real number line. It can have any value. Some exam The set of real numbers, denoted by <math>\mathbb{R}</math>, is a subset of [[complex number]]s(<math>\mathbb{C}</math>). Commonly used subse
  3 KB (496 words) - 23:22, 5 January 2022
• Euclidean algorithm
  ...orithm that finds the [[greatest common divisor]] (GCD) of two elements of a [[Euclidean domain]], the most common of which is the [[nonnegative]] [[int ...c idea is to repeatedly use the fact that <math>\gcd({a,b}) \equiv \gcd({b,a - b})</math>
  6 KB (924 words) - 21:50, 8 May 2022
• Binomial Theorem
  The '''Binomial Theorem''' states that for [[real]] or [[complex]] <math>a</math>, <math>b</math>, and [[non-negative]] [[integer]] <math>n</math>, <center><math>(a+b)^n = \sum_{k=0}^{n}\binom{n}{k}a^{n-k}b^k</math></center>
  5 KB (935 words) - 13:11, 20 February 2024
• Prime number
  A '''prime number''' (or simply '''prime''') is a [[positive integer]] <math>p>1</math> whose only positive [[divisor | divis ...</math> must [[#Importance of Primes|have]] a prime factor, which leads to a direct contradiction.
  6 KB (985 words) - 12:38, 25 February 2024
• Function
  A '''function''' is a rule that maps one set of values to another set of values, assigning to eac ...is a ''function from <math>A</math> to <math>B</math>'' (written <math>f: A \to B</math>) if and only if
  10 KB (1,761 words) - 03:16, 12 May 2023
• Complementary counting
  ...ting may lead to a quick solution is the phrase "not" or "at least" within a problem statement. ...is the [[complement]] of <math>B</math>. In most instances, though, <math>A</math> is obvious from context and is committed from mention.
  8 KB (1,192 words) - 17:20, 16 June 2023
• Combinatorial identity
  ...> objects must have some <math>0\le k\le r</math> objects from group <math>m</math> and the remaining from group <math>n</math>. .... Think of the left hand side as picking <math>k</math> men from the <math>m</math> total men and picking <math>r-k</math> women from the <math>n</math>
  12 KB (1,996 words) - 12:01, 18 May 2024
• Circle
  A '''circle''' is a geometric figure commonly used in Euclidean [[geometry]]. {{asy image|<asy>unitsize(2cm);draw(unitcircle,blue);</asy>|right|A basic circle.}}
  9 KB (1,581 words) - 18:59, 9 May 2024
• Ellipse
  An '''ellipse''' is a type of [[conic section]]. An ellipse is formed by cutting through a [[cone]] at an [[angle]].
  5 KB (892 words) - 21:52, 1 May 2021
• Divisor
  ...hat <math>n=kd</math> or, in other words, if <math>\frac nd</math> is also a natural number (i.e <math>d</math> divides <math>n</math>). See [[Divisibil A common notation to indicate a number is a divisor of another is <math>n|k</math>. This means that <math>n</math> divi
  1 KB (274 words) - 19:50, 29 August 2023
• Base numbers
  ...each number in 2746 is actually just a placeholder which shows how many of a certain power of 10 there are. The first digit to the left of the decimal ...digits 0-9. Usually, the base, or '''radix''', of a number is denoted as a subscript written at the right end of the number (e.g. in our example above
  4 KB (547 words) - 17:23, 30 December 2020
• Multiple
  ...m</math> and <math>n</math> are integers. (In this case, <math>k</math> is a multiple of <math>n</math>, as well). .../math> exactly when <math>k</math> is [[divisibility | divisble by]] <math>m</math>.
  860 bytes (142 words) - 22:51, 26 January 2021
• Median of a triangle
  A '''median''' of a [[triangle]] is a [[cevian]] of the triangle that joins one [[vertex]] to the [[midpoint]] of In the following figure, <math>AM</math> is a median of triangle <math>ABC</math>.
  1 KB (185 words) - 20:24, 6 March 2024
• Pi
  Pi is the [[ratio]] of the [[circumference]] ([[perimeter]]) of a given [[circle]] to its [[diameter]]. It is approximately equal to 3.14159 ...i</math> is to inscribe a unit circle in a square of side length 2. Using a computer, random points are placed inside the square. Because the area of
  8 KB (1,469 words) - 21:11, 16 September 2022
• Fibonacci sequence
  The '''Fibonacci sequence''' is a [[sequence]] of [[integer]]s in which the first and second terms are both e ...th> for <math>n \geq 3</math>. This is the simplest nontrivial example of a [[linear recursion]] with constant coefficients. There is also an explicit
  6 KB (957 words) - 23:49, 7 March 2024

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