Fungrim home page

Fungrim entry: 775e10

φ(m)φ(n)φ ⁣(mn)\varphi(m) \varphi(n) \le \varphi\!\left(m n\right)
Assumptions:mZ0  and  nZ0m \in \mathbb{Z}_{\ge 0} \;\mathbin{\operatorname{and}}\; n \in \mathbb{Z}_{\ge 0}
\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}
Fungrim symbol Notation Short description
Totientφ(n)\varphi(n) Euler totient function
ZZGreaterEqualZn\mathbb{Z}_{\ge n} Integers greater than or equal to n
Source code for this entry:
    Formula(LessEqual(Mul(Totient(m), Totient(n)), Totient(Mul(m, 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