Euler's totient function
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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
Jordan's totient function — In number theory, Jordan s totient function J k(n) of a positive integer n is the number of k tuples of positive integers all less than or equal to n that form a coprime ( k + 1) tuple together with n . This is a generalisation of Euler s totient … Wikipedia
Carmichael's totient function conjecture — In mathematics, Carmichael s totient function conjecture concerns the multiplicity of values of Euler s totient function phi;( n ), which counts the number of integers less than and coprime to n .This function phi;( n ) is equal to 2 when n is… … Wikipedia
Euler–Mascheroni constant — Euler s constant redirects here. For the base of the natural logarithm, e ≈ 2.718..., see e (mathematical constant). The area of the blue region is equal to the Euler–Mascheroni constant. List of numbers – Irrational and suspected irrational… … 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
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
List of topics named after Leonhard Euler — In mathematics and physics, there are a large number of topics named in honour of Leonhard Euler (pronounced Oiler ). As well, many of these topics include their own unique function, equation, formula, identity, number (single or sequence), or… … Wikipedia
Divisor function — σ0(n) up to n = 250 Sigma function σ … Wikipedia
Highly totient number — A highly totient number k is an integer that has more solutions to the equation φ( x ) = k , where φ is Euler s totient function, than any integer below it. The first few highly totient numbers are1, 2, 4, 8, 12, 24, 48, 72, 144, 240, 432, 480,… … Wikipedia
Carmichael function — In number theory, the Carmichael function of a positive integer n, denoted lambda(n),is defined as the smallest positive integer m such that:a^m equiv 1 pmod{n}for every integer a that is coprime to n.In other words, in more algebraic terms, it… … Wikipedia
