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• Lagrange's Theorem
  '''Lagrange's theorem''' is a result on the indices of [[coset]]s of a [[group]]. so the index and order of <math>H</math> are [[divisor]]s of <math>g</math>.
  2 KB (303 words) - 12:24, 9 April 2019
• Burnside's Lemma
  ...rial]] result in [[group theory]] that is useful for counting the [[orbit]]s of a [[set]] on which a [[group]] [[group action|acts]]. ...led the '''Cauchy-Frobenius Lemma''', or '''the lemma that is not Burnside's'''. The lemma was (mistakenly) attributed to Burnside because he quoted an
  5 KB (757 words) - 18:11, 23 October 2023
• Cayley's Theorem
  ...characterizes group structure as the structure of a family of [[bijection]]s.
  1 KB (214 words) - 16:56, 19 February 2024
• Legendre's Formula
  '''Legendre's Formula''' states that ...of <math>n!</math> and <math>S_p(n)</math> is the [[sum]] of the [[digit]]s of <math>n</math> when written in [[base]] <math>p</math>.
  4 KB (699 words) - 17:55, 5 August 2023
• Routh's Theorem
  ...be the intersection of <math>CF</math> and <math>AD</math>. Then, '''Routh's Theorem''' states that <cmath>[GHI]=\dfrac{(rst-1)^2}{(rs+r+1)(st+s+1)(tr+t+1)}[ABC]</cmath>
  2 KB (267 words) - 00:02, 24 March 2021
• Bezout's Lemma
  #REDIRECT[[Bézout's Identity]]
  31 bytes (4 words) - 13:34, 3 May 2023
• Carnot's Theorem
  '''Carnot's Theorem''' states that in a [[triangle]] <math>ABC</math>, the signed sum o label("$O_C$",f,S);
  4 KB (723 words) - 01:45, 18 February 2021
• Karamata's Inequality
  '''Karamata's Inequality''' states that if <math>(a_i)</math> [[Majorization|majorizes]] ...ming <math>a_i\geq a_{i+1}</math> and similarily with the <math>b_i</math>'s, we get that <math>c_i\geq c_{i+1}</math>. Now, we know:
  2 KB (370 words) - 03:39, 28 March 2024
• Aczel's Inequality
  '''Aczél's Inequality''' states that if <math>a_1^2>a_2^2+\cdots +a_n^2</math> or <mat * Popoviciu, T., Sur quelques inégalités, Gaz. Mat. Fiz. Ser. A, 11 (64) (1959) 451–461
  2 KB (428 words) - 16:36, 29 December 2021
• Gauss's Lemma
  * [[Gauss's Lemma (polynomial)]] * [[Quadratic reciprocity|Gauss's Lemma (quadratic reciprocity)]]
  292 bytes (32 words) - 13:14, 30 September 2020
• Gauss's Lemma (polynomial)
  '''Gauss's Lemma for Polynomials''' is a result in [[abstract algebra | algebra]]. The original statement concerns [[polynomial]]s with [[integer]] coefficients. Such a polynomial is called ''primitive'' i
  3 KB (483 words) - 12:23, 30 May 2019
• Fermat's Two Squares Theorem
  '''Fermat's Two Squares Theorem''' states that that a [[prime number]] <math>p</math> c Since 0 and 1 are the only [[quadratic residue]]s mod 4, it follows that if <math>p</math> is a prime number represented as t
  4 KB (612 words) - 12:10, 30 May 2019
• De Morgan's Laws
  '''De Morgan's Laws''' are two very important laws in the fields of [[set theory]] and [[b
  3 KB (448 words) - 19:53, 19 February 2022
• Van Aubel's Theorem
  ...; yielding centers <math>P_{AB}, P_{BC}, P_{CD}, P_{DA}</math>. Van Aubel's Theorem states that the two line segments connecting opposite centers are p dot("$q$",Q,S);
  2 KB (410 words) - 14:01, 4 March 2023
• Ballemy's Theorem
  82 bytes (17 words) - 19:19, 11 June 2024
• Bolzano's theorem
  '''Bolzano's Theorem''' is a special case of the [[Intermediate Value Theorem]], where <
  225 bytes (34 words) - 12:18, 30 May 2019
• Cauchy's Integral Formula
  '''Cauchy's Integral Formula''' is a fundamental result in by application of [[Cauchy's Integral Theorem]].
  4 KB (689 words) - 17:19, 18 January 2024
• L'Hopital's Rule
  #REDIRECT [[L'Hôpital's Rule]]
  31 bytes (4 words) - 21:27, 11 March 2022
• Liouville's Theorem (complex analysis)
  In [[complex analysis]], '''Liouville's Theorem''' states that a [[Picard's Little Theorem]] is a stronger result.
  2 KB (412 words) - 20:30, 16 January 2024
• Hilbert's Basis Theorem
  '''Hilbert's Basis Theorem''' is a result concerning [[Noetherian]] [[ring]]s. It states that if <math>A</math> is a (not necessarily [[commutative]])
  4 KB (617 words) - 19:59, 23 April 2023

Page text matches

• Geometric mean
  ...tric mean''' of a collection of <math>n</math> [[positive]] [[real number]]s is the <math>n</math>th [[root]] of the product of the numbers. Note that MC("a",D((-5,-0.3)--(3,-0.3),black,Arrows),S);
  2 KB (282 words) - 22:04, 11 July 2008
• Principle of Inclusion-Exclusion
  ...set]]s, the size of each set, and the size of all possible [[intersection]]s among the sets. Now, for <math>|A\cap B|</math>, that's just putting four guys in order. By the same logic as above, this is <math>
  9 KB (1,703 words) - 07:25, 24 March 2024
• Mill's Constant
  Mill's Constant is defined as the smallest real number <math>\theta</math> such th ...smallest element in that set. If the [[Riemann Hypothesis]] is true, Mill's constant is approximately <math>1.3063778838630806904686144926...</math> an
  794 bytes (105 words) - 01:59, 15 January 2022
• Combination
  ...ly that you choose the rest. This identity is also the reason why [[Pascal's Triangle]] is symmetrical. * [[Pascal's Triangle]]
  4 KB (615 words) - 11:43, 21 May 2021
• Cauchy-Schwarz Inequality
  Its elementary algebraic formulation is often referred to as '''Cauchy's Inequality''' and states that for any list of reals <math>a_1, a_2, \ldots, ...as Sedrakyan's Inequality, Bergström's Inequality, Engel's Form or Titu's Lemma the following inequality is a direct result of Cauchy-Schwarz inequal
  13 KB (2,048 words) - 15:28, 22 February 2024
• Discriminant
  ...use if the discriminant is positive, the equation has two [[real]] [[root]]s; if the discriminant is negative, the equation has two [[nonreal]] roots; a ...s a polynomial of degree 3, which also makes possible to us to use Cardano's formula, by doing the substitution <math>x=z-\frac{a}{3}</math> on the poly
  4 KB (768 words) - 17:56, 24 June 2024
• Ceva's Theorem
  #REDIRECT[[Ceva's theorem]]
  27 bytes (3 words) - 16:06, 9 May 2021
• Menelaus' theorem
  First let's define some masses. * [[Ceva's theorem]]
  5 KB (804 words) - 03:01, 12 June 2023
• Number theory
  ...cs]] associated with studying the properties and identities of [[ integer]]s. *[[Prime number]]s
  3 KB (399 words) - 23:08, 8 January 2024
• Number theory/Intermediate
  ** [[Simon's Favorite Factoring Trick]] ** [[Euler's Totient Theorem]]
  1,016 bytes (108 words) - 21:05, 26 January 2016
• San Diego ARML
  Individually, San Diego Surf had 2 students who scored 7's and went to tiebreakers: In addition, there were multiple students (on both teams) who scored 6's and earned medals as team high scorers:
  2 KB (378 words) - 16:34, 5 January 2010
• ARML historical results
  | [[New York City ARML]] (New York City S)
  20 KB (2,642 words) - 21:23, 1 June 2024
• Fermat's Little Theorem
  '''Fermat's Little Theorem''' is highly useful in [[number theory]] for simplifying the A frequently used corollary of Fermat's Little Theorem is <math>a^p \equiv a \pmod {p}</math>. As you can see, it i
  16 KB (2,658 words) - 16:02, 8 May 2024
• Chebyshev's Inequality
  '''Chebyshev's inequality''', named after [[Pafnuty Chebyshev]], states that if ...nce of the [[Rearrangement inequality]], which gives us that the sum <math>S=a_1b_{i_1}+a_2b_{i_2}+...+a_nb_{i_n} </math> is maximal when <math>i_k=k</m
  1 KB (214 words) - 20:32, 13 March 2022
• Euler's Totient Theorem
  '''Euler's Totient Theorem''' is a theorem closely related to his [[totient function]] Let <math>\phi(n)</math> be [[Euler's totient function]]. If <math>n</math> is a positive integer, <math>\phi{(n)
  3 KB (542 words) - 17:45, 21 March 2023
• Geometric inequality
  ...[inequality]] involving various measures ([[angle]]s, [[length]]s, [[area]]s, etc.) in [[geometry]]. ...equality extends this to [[obtuse triangle| obtuse]] and [[acute triangle]]s. The inequality says:
  7 KB (1,296 words) - 14:22, 22 October 2023
• Brahmagupta's Formula
  .../math>, <math>c</math>, <math>d</math> are the four side lengths and <math>s = \frac{a+b+c+d}{2}</math>. <cmath>16[ABCD]^2=16(s-a)(s-b)(s-c)(s-d)</cmath>
  3 KB (465 words) - 18:31, 3 July 2023
• Ptolemy's Theorem
  #REDIRECT[[Ptolemy's theorem]]
  30 bytes (3 words) - 17:37, 9 May 2021
• Ptolemy's theorem
  ...[equality condition | equality case]] of [[Ptolemy's Inequality]]. Ptolemy's theorem frequently shows up as an intermediate step in problems involving i ...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
• Elementary symmetric sum
  .../en.wikipedia.org/wiki/Sums_of_powers sums of powers], combined with Vieta's formulas. Elementary symmetric sums show up in [[Vieta's formulas]]. In a monic polynomial of degree <math>n</math>, the coefficient
  2 KB (275 words) - 12:51, 26 July 2023

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