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...

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...

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 ) = {...

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...

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

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

{\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...

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...

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...

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...

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...

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

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...

> 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...

its conjugate. The related function z ↦ − s ( − 1 / z ) {\textstyle z\mapsto -s\left(-1/z\right)} is the generating function for the negafibonacci numbers...

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...

omega functions Almost prime Semiprime Euler's totient function Highly cototient Highly totient Noncototient Nontotient Perfect totient Sparsely totient Aliquot...

also highly totient, as is 576, the square of 24. While 17 different integers have a totient value of 72, the sum of Euler's totient function φ(x) over...

ϕ ∗ 1 = Id {\displaystyle \phi *1={\text{Id}}} , proved under Euler's totient function. ϕ = Id ∗ μ {\displaystyle \phi ={\text{Id}}*\mu } , by Möbius...

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...

g., multiplying rotations by 3. Compare the values 6 and 4 for Euler's totient function, the multiplicative group of integers modulo n for n = 9 and 10...

/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...

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...