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Euler's Theorem

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  • Euler's theorem — In number theory, Euler s theorem (also known as the Fermat Euler theorem or Euler s totient theorem) states that if n is a positive integer and a is coprime to n , then:a^{varphi (n)} equiv 1 pmod{n}where φ( n ) is Euler s totient function and …   Wikipedia

  • Euler's theorem (differential geometry) — In the mathematical field of differential geometry, Euler s theorem is a result on the curvature of curves on a surface. The theorem establishes the existence of principal curvatures and associated principal directions which give the directions… …   Wikipedia

  • Euler's theorem in geometry — In geometry, Euler s theorem, named after Leonhard Euler, states that the distance d between the circumcentre and incentre of a triangle can be expressed as : d^2=R (R 2r) ,where R and r denote the circumradius and inradius respectively (the… …   Wikipedia

  • Euler'sches Theorem — Ausschöpfungstheorem, Adding up Theorem. Bei linear homogenen Produktionsfunktionen gilt: wobei: f´i = partielle Grenzproduktivität des Faktors i, ri = gesamte Einsatzmenge des Faktors i, Q = Output. Bei vollständiger Konkurrenz ist das… …   Lexikon der Economics

  • Euler's totient function — For other functions named after Euler, see List of topics named after Leonhard Euler. The first thousand values of φ(n) In number theory, the totient φ(n) of a positive integer n is defined to be the number of positive integers less than or equal …   Wikipedia

  • Euler's formula — This article is about Euler s formula in complex analysis. For Euler s formula in algebraic topology and polyhedral combinatorics see Euler characteristic.   Part of a series of articles on The mathematical constant e …   Wikipedia

  • Euler's rotation theorem — In kinematics, Euler s rotation theorem states that, in three dimensional space, any displacement of a rigid body such that a point on the rigid body remains fixed, is equivalent to a rotation about a fixed axis through that point. The theorem is …   Wikipedia

  • Euler-Bernoulli beam equation — Euler Bernoulli beam theory, or just beam theory, is a simplification of the linear theory of elasticity which provides a means of calculating the load carrying and deflection characteristics of beams. It was first enunciated circa 1750, but was… …   Wikipedia

  • Euler's sum of powers conjecture — Euler s conjecture is a disproved conjecture in mathematics related to Fermat s last theorem which was proposed by Leonhard Euler in 1769. It states that for all integers n and k greater than 1, if the sum of n k th powers of positive integers is …   Wikipedia

  • Euler's criterion — In mathematics, Euler s criterion is used in determining in number theory whether a given integer is a quadratic residue modulo a prime. DefinitionEuler s criterion states: Let p be an odd prime and a an integer coprime to p . Then a is a… …   Wikipedia

  • Euler pseudoprime — An odd composite integer n is called an Euler pseudoprime to base a , if a and n are coprime, and : a^{(n 1)/2} equiv pm 1pmod{n}(where mod refers to the modulo operation).The motivation for this definition is the fact that all prime numbers p… …   Wikipedia

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