Fungrim home page

Fungrim entry: 05e9ae

φ ⁣(mn)=mn1φ ⁣(m)\varphi\!\left({m}^{n}\right) = {m}^{n - 1} \varphi\!\left(m\right)
Assumptions:mZ0andnZ1m \in \mathbb{Z}_{\ge 0} \,\mathbin{\operatorname{and}}\, n \in \mathbb{Z}_{\ge 1}
TeX:
\varphi\!\left({m}^{n}\right) = {m}^{n - 1} \varphi\!\left(m\right)

m \in \mathbb{Z}_{\ge 0} \,\mathbin{\operatorname{and}}\, n \in \mathbb{Z}_{\ge 1}
Definitions:
Fungrim symbol Notation Short description
Totientφ ⁣(n)\varphi\!\left(n\right) Euler totient function
Powab{a}^{b} Power
ZZGreaterEqualZn\mathbb{Z}_{\ge n} Integers greater than or equal to n
Source code for this entry:
Entry(ID("05e9ae"),
    Formula(Equal(Totient(Pow(m, n)), Mul(Pow(m, Sub(n, 1)), Totient(m)))),
    Variables(m, n),
    Assumptions(And(Element(m, ZZGreaterEqual(0)), Element(n, ZZGreaterEqual(1)))))

Topics using this entry

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

2019-08-17 11:32:46.829430 UTC