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...

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...

totient function, and the least universal exponent function. The order of the multiplicative group of integers modulo n is φ(n), where φ is Euler's totient...

number theory, the totient summatory function Φ ( n ) {\displaystyle \Phi (n)} is a summatory function of Euler's totient function defined by: Φ ( n )...

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...

been given simple yet 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...

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...

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...

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...

In mathematics, Carmichael's totient function conjecture concerns the multiplicity of values of Euler's totient function φ(n), which counts the number...

expansion of the gamma function for small arguments. An inequality for Euler's totient function The growth rate of the divisor function In dimensional regularization...

equal to φ - 1.) Euler's totient function φ(n) in number theory; also called Euler's phi function. The cyclotomic polynomial functions Φn(x) of algebra...

λ(n) is equal to the Euler totient function of n; for powers of 2 greater than 4 it is equal to one half of the Euler totient function of n: λ ( n ) = {...

lists a few identities involving the divisor functions Euler's totient function, Euler's phi function Refactorable number Table of divisors Unitary divisor...

elements, no two elements of R are congruent modulo n. Here φ denotes Euler's totient function. A reduced residue system modulo n can be formed from a complete...

a^{\phi (m)}\equiv 1{\pmod {m}},} where ϕ {\displaystyle \phi } is Euler's totient function. This follows from the fact that a belongs to the multiplicative...

of e {\displaystyle e} modulo ϕ ( n ) {\displaystyle \phi (n)} (Euler's totient function of n {\displaystyle n} ) is the trapdoor: f ( x ) = x e mod n ...

following 899 and preceding 901. It is the square of 30 and the sum of Euler's totient function for the first 54 positive integers. In base 10, it is a Harshad...

{\displaystyle n=pq} (with p ≠ q {\displaystyle p\neq q} ) the value of Euler's totient function φ ( n ) {\displaystyle \varphi (n)} (the number of positive integers...

ideal system of coins. In number theory, all powers of three are perfect totient numbers. The sums of distinct powers of three form a Stanley sequence,...

mathematics) In mathematics, Lehmer's totient problem asks whether there is any composite number n such that Euler's totient function φ(n) divides n − 1. This is...

The Riemann zeta function or Euler–Riemann zeta function, denoted by the Greek letter ζ (zeta), is a mathematical function of a complex variable defined...

{p^{\alpha }}}} where ϕ ( n ) {\displaystyle \phi (n)} is the Euler's totient function. The Euler numbers grow quite rapidly for large indices as they have...

{\displaystyle n} with exactly nine solutions to the equation Euler's totient function φ ( x ) = n {\displaystyle \varphi (x)=n} (for values 41, 55, 75...

the number 1: for instance, the formulas for Euler's totient function or for the sum of divisors function are different for prime numbers than they are...

unique. The number of primitive elements is φ(q − 1) where φ is Euler's totient function. The result above implies that xq = x for every x in GF(q). The...

the origin (zero point) Sigma function: Sums of powers of divisors of a given natural number. Euler's totient function: Number of numbers coprime to (and...

a natural number n such that n and φ(n) are coprime. Here φ is Euler's totient function. An equivalent definition is that a number n is cyclic if and only...

{Z} } ) = {ax + b | (a, n) = 1} and has order nϕ(n), where ϕ is Euler's totient function, the number of k in 1, ..., n − 1 coprime to n. It can be understood...

squares as a sum of squares Cubic number – Number raised to the third power Euler's four-square identity – Product of sums of four squares expressed as a sum...