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Fungrim entry: 1d731f

φ ⁣(pk)=pk1(p1)\varphi\!\left({p}^{k}\right) = {p}^{k - 1} \left(p - 1\right)
Assumptions:pPandkZ1p \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
Totientφ ⁣(n)\varphi\!\left(n\right) Euler totient function
Powab{a}^{b} Power
PPP\mathbb{P} Prime numbers
ZZGreaterEqualZn\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)))))

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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