Fungrim entry: 1d731f

\varphi\!\left({p}^{k}\right) = {p}^{k - 1} \left(p - 1\right)

Assumptions:

p \in \mathbb{P} \;\mathbin{\operatorname{and}}\; k \in \mathbb{Z}_{\ge 1}

TeX:

\varphi\!\left({p}^{k}\right) = {p}^{k - 1} \left(p - 1\right)

p \in \mathbb{P} \;\mathbin{\operatorname{and}}\; k \in \mathbb{Z}_{\ge 1}

Definitions:

Fungrim symbol	Notation	Short description
`Totient`	$\varphi(n)$	Euler totient function
`Pow`	${a}^{b}$	Power
`PP`	$\mathbb{P}$	Prime numbers
`ZZGreaterEqual`	$\mathbb{Z}_{\ge n}$	Integers greater than or equal to n

Source code for this entry:

Entry(ID("1d731f"),
    Formula(Equal(Totient(Pow(p, k)), Mul(Pow(p, Sub(k, 1)), Sub(p, 1)))),
    Variables(p, k),
    Assumptions(And(Element(p, PP), Element(k, ZZGreaterEqual(1)))))

Topics using this entry

Totient function

Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2021-03-15 19:12:00.328586 UTC