Fungrim home page

Fungrim entry: 08fb81

φ ⁣(mn)≤mφ(n)\varphi\!\left(m n\right) \le m \varphi(n)
Assumptions:m∈Z≥0  and⁡  n∈Z≥0m \in \mathbb{Z}_{\ge 0} \;\mathbin{\operatorname{and}}\; n \in \mathbb{Z}_{\ge 0}
TeX:
\varphi\!\left(m n\right) \le m \varphi(n)

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("08fb81"),
    Formula(LessEqual(Totient(Mul(m, n)), Mul(m, Totient(n)))),
    Variables(m, n),
    Assumptions(And(Element(m, ZZGreaterEqual(0)), Element(n, ZZGreaterEqual(0)))))

Topics using this entry

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