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proofs of identity

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  • Proofs of trigonometric identities — are used to show relations between trigonometric functions. This article will list trigonometric identities and prove them.Elementary trigonometric identitiesDefinitionsReferring to the diagram at the right, the six trigonometric functions of… …   Wikipedia

  • Proofs of Fermat's theorem on sums of two squares — Fermat s theorem on sums of two squares asserts that an odd prime number p can be expressed as: p = x^2 + y^2with integer x and y if and only if p is congruent to 1 (mod 4). The statement was announced by Fermat in 1640, but he supplied no proof …   Wikipedia

  • Proofs involving the totient function — This page provides proofs for identities involving the totient function varphi(k) and the Möbius function mu(k).um of integers relatively prime to and less than or equal to n Claim::sum {1le kle n atop {gcd(k,n)=1 k = frac{1}{2} , varphi(n) ,… …   Wikipedia

  • Proofs of Fermat's little theorem — This article collects together a variety of proofs of Fermat s little theorem, which states that:a^p equiv a pmod p ,!for every prime number p and every integer a (see modular arithmetic). Simplifications Some of the proofs of Fermat s little… …   Wikipedia

  • Addition of natural numbers/Proofs — Mathematical proofs for addition of the natural numbers: additive identity, commutativity, and associativity. These proofs are used in the article Addition of natural numbers.DefinitionsThis article will use the definitions in addition of natural …   Wikipedia

  • List of mathematical proofs — A list of articles with mathematical proofs:Theorems of which articles are primarily devoted to proving them: See also: *Bertrand s postulate and a proof *Estimation of covariance matrices *Fermat s little theorem and some proofs *Gödel s… …   Wikipedia

  • Additive identity — In mathematics the additive identity of a set which is equipped with the operation of addition is an element which, when added to any element x in the set, yields x . One of the most familiar additive identities is the number 0 from elementary… …   Wikipedia

  • Pythagorean trigonometric identity — The Pythagorean trigonometric identity is a trigonometric identity expressing the Pythagorean theorem in terms of trigonometric functions. Along with the sum of angles formulae (see Angle sum and difference identities) it is the basic relation… …   Wikipedia

  • A curious identity involving binomial coefficients — In combinatorics, a curious identity by Sun is the following combinatorial identity involving binomial coefficients first established by Zhi Wei Sun in 2002::(x+m+1)sum {i=0}^m( 1)^idbinom{x+y+i}{m i}dbinom{y+2i}{i} sum {i=0}^{m}dbinom{x+i}{m i}( …   Wikipedia

  • Dixon's identity — In mathematics, Dixon s identity (or Dixon s theorem or Dixon s formula) is any of several different but closely related identities proved by A. C. Dixon, some involving finite sums of products of three binomial coefficients, and some evaluating… …   Wikipedia

  • Lewis Carroll identity — The Lewis Carroll identity is an identity involving minors of a square matrix proved by Charles Dodgson (pseudonym Lewis Carroll), who used it in a method of numerical evaluation of matrix determinants called the Dodgson condensation. From the… …   Wikipedia

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