also referred to as Euler's totient function, the Euler totient, or Euler's totient. Jordan's totient is a generalization of Euler's. The cototient of n...
44 KB (6,473 words) - 16:27, 10 June 2024
denotes Euler's totient function; that is a φ ( n ) ≡ 1 ( mod n ) . {\displaystyle a^{\varphi (n)}\equiv 1{\pmod {n}}.} In 1736, Leonhard Euler published...
9 KB (1,149 words) - 18:09, 9 June 2024
Moreover, Euler's totient function at 5 is 4, φ(5) = 4, because there are exactly 4 numbers less than and coprime to 5 (1, 2, 3, and 4). Euler's theorem...
22 KB (3,192 words) - 16:54, 10 March 2024
Jordan's totient function is a generalization of Euler's totient function, which is the same as J 1 ( n ) {\displaystyle J_{1}(n)} . The function is named...
6 KB (921 words) - 23:18, 29 March 2024
number theory, the totient summatory function Φ ( n ) {\displaystyle \Phi (n)} is a summatory function of Euler's totient function defined by: Φ ( n )...
3 KB (526 words) - 07:27, 4 July 2022
been given simple and ambiguous names such as Euler's function, Euler's equation, and Euler's formula. Euler's work touched upon so many fields that he is...
14 KB (1,603 words) - 16:45, 2 July 2024
In mathematics, Carmichael's totient function conjecture concerns the multiplicity of values of Euler's totient function φ(n), which counts the number...
8 KB (839 words) - 17:54, 27 March 2024
then ap−1 ≡ 1 (mod p). Euler's theorem: If a and m are coprime, then aφ(m) ≡ 1 (mod m), where φ is Euler's totient function. A simple consequence of...
29 KB (3,589 words) - 22:14, 12 July 2024
where ϕ {\displaystyle \phi } is Euler's totient function, than any integer smaller than it. The first few highly totient numbers are 1, 2, 4, 8, 12, 24...
3 KB (370 words) - 12:16, 27 March 2024
group (also called multiplicative group of integers modulo n) and Euler's totient function. The primitive residue class group of a modulus z is defined as...
35 KB (4,795 words) - 03:23, 20 December 2023