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Fungrim entry: 05e9ae

φ ⁣(mn)=mn−1φ(m)\varphi\!\left({m}^{n}\right) = {m}^{n - 1} \varphi(m)
Assumptions:m∈Z≥0  and⁡  n∈Z≥1m \in \mathbb{Z}_{\ge 0} \;\mathbin{\operatorname{and}}\; n \in \mathbb{Z}_{\ge 1}
TeX:
\varphi\!\left({m}^{n}\right) = {m}^{n - 1} \varphi(m)

m \in \mathbb{Z}_{\ge 0} \;\mathbin{\operatorname{and}}\; n \in \mathbb{Z}_{\ge 1}
Definitions:
Fungrim symbol Notation Short description
Totientφ(n)\varphi(n) Euler totient function
Powab{a}^{b} Power
ZZGreaterEqualZ≥n\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)))))

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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