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...

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

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...

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...

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...

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...

number of its elements shall be denoted by ϕ(z) (analogously to Euler's totient function φ(n) for integers n). For Gaussian primes it immediately follows...

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 ) = {...

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

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...

Bessel functions. Asymptotic expansions of modified Struve functions. In relation to other special functions. An inequality for Euler's totient function. The...

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...

{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...

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...

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...

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...

theory, a perfect totient number is an integer that is equal to the sum of its iterated totients. That is, one applies the totient function to a number n...

{\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,...

nontotient is a positive integer n which is not a totient number: it is not in the range of Euler's totient function φ, that is, the equation φ(x) = n has no solution...

}{n}}\right)} whose degree is ϕ ( n ) {\displaystyle \phi (n)} , Euler's totient function at n {\displaystyle n} . Then, the splitting field over Q {\displaystyle...

{\displaystyle \mathbb {F} _{q},} where φ {\displaystyle \varphi } is Euler's totient function. In F q , {\displaystyle \mathbb {F} _{q},} the freshman's dream...

{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...

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...

testing. It is an abelian, finite group whose order is given by Euler's totient function: | ( Z / n Z ) × | = φ ( n ) . {\displaystyle |(\mathbb {Z} /n\mathbb...

numbers. 266 is a nontotient number which is an even number not in Euler’s totient function. 266 is an inconsummate number. "Facts about the integer". Wolfram...

generating function of the Fibonacci sequence, ∑ i = 0 ∞ F i z i {\displaystyle \sum _{i=0}^{\infty }F_{i}z^{i}} , is the rational function z 1 − z − z...

> 1. From this, we can relate the lengths of Fn and Fn−1 using Euler's totient function φ(n): | F n | = | F n − 1 | + φ ( n ) . {\displaystyle |F_{n}|=|F_{n-1}|+\varphi...