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Fungrim entry: eae0de

(mn)    (φ ⁣(m)φ ⁣(n))\left(m \mid n\right) \implies \left(\varphi\!\left(m\right) \mid \varphi\!\left(n\right)\right)
Assumptions:mZ0andnZ0m \in \mathbb{Z}_{\ge 0} \,\mathbin{\operatorname{and}}\, n \in \mathbb{Z}_{\ge 0}
TeX:
\left(m \mid n\right) \implies \left(\varphi\!\left(m\right) \mid \varphi\!\left(n\right)\right)

m \in \mathbb{Z}_{\ge 0} \,\mathbin{\operatorname{and}}\, n \in \mathbb{Z}_{\ge 0}
Definitions:
Fungrim symbol Notation Short description
Totientφ ⁣(n)\varphi\!\left(n\right) Euler totient function
ZZGreaterEqualZn\mathbb{Z}_{\ge n} Integers greater than or equal to n
Source code for this entry:
Entry(ID("eae0de"),
    Formula(Implies(Divides(m, n), Divides(Totient(m), Totient(n)))),
    Variables(m, n),
    Assumptions(And(Element(m, ZZGreaterEqual(0)), Element(n, ZZGreaterEqual(0)))))

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

2019-08-19 14:38:23.809000 UTC