# Fungrim entry: 56d7fe

$\varphi\!\left(m n\right) = \frac{\varphi(m) \varphi(n) \gcd\!\left(m, n\right)}{\varphi\!\left(\gcd\!\left(m, n\right)\right)}$
Assumptions:$m \in \mathbb{Z}_{\ge 1} \;\mathbin{\operatorname{and}}\; n \in \mathbb{Z}_{\ge 1}$
TeX:
\varphi\!\left(m n\right) = \frac{\varphi(m) \varphi(n) \gcd\!\left(m, n\right)}{\varphi\!\left(\gcd\!\left(m, n\right)\right)}

m \in \mathbb{Z}_{\ge 1} \;\mathbin{\operatorname{and}}\; n \in \mathbb{Z}_{\ge 1}
Definitions:
Fungrim symbol Notation Short description
Totient$\varphi(n)$ Euler totient function
GCD$\gcd\!\left(a, b\right)$ Greatest common divisor
ZZGreaterEqual$\mathbb{Z}_{\ge n}$ Integers greater than or equal to n
Source code for this entry:
Entry(ID("56d7fe"),
Formula(Equal(Totient(Mul(m, n)), Div(Mul(Mul(Totient(m), Totient(n)), GCD(m, n)), Totient(GCD(m, n))))),
Variables(m, n),
Assumptions(And(Element(m, ZZGreaterEqual(1)), Element(n, ZZGreaterEqual(1)))))

## 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