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Fungrim entry: 775e10

φ(m)φ(n)≤φ ⁣(mn)\varphi(m) \varphi(n) \le \varphi\!\left(m n\right)
Assumptions:m∈Z≥0  and⁡  n∈Z≥0m \in \mathbb{Z}_{\ge 0} \;\mathbin{\operatorname{and}}\; n \in \mathbb{Z}_{\ge 0}
TeX:
\varphi(m) \varphi(n) \le \varphi\!\left(m n\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(n) Euler totient function
ZZGreaterEqualZ≥n\mathbb{Z}_{\ge n} Integers greater than or equal to n
Source code for this entry:
Entry(ID("775e10"),
    Formula(LessEqual(Mul(Totient(m), Totient(n)), Totient(Mul(m, 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.

2021-03-15 19:12:00.328586 UTC