# Fungrim entry: 499cfc

$\gcd\!\left({p}^{m}, {q}^{n}\right) = 1$
Assumptions:$p \in \mathbb{P} \;\mathbin{\operatorname{and}}\; q \in \mathbb{P} \;\mathbin{\operatorname{and}}\; p \ne q \;\mathbin{\operatorname{and}}\; m \in \mathbb{Z}_{\ge 0} \;\mathbin{\operatorname{and}}\; n \in \mathbb{Z}_{\ge 0}$
TeX:
\gcd\!\left({p}^{m}, {q}^{n}\right) = 1

p \in \mathbb{P} \;\mathbin{\operatorname{and}}\; q \in \mathbb{P} \;\mathbin{\operatorname{and}}\; p \ne q \;\mathbin{\operatorname{and}}\; m \in \mathbb{Z}_{\ge 0} \;\mathbin{\operatorname{and}}\; n \in \mathbb{Z}_{\ge 0}
Definitions:
Fungrim symbol Notation Short description
GCD$\gcd\!\left(a, b\right)$ Greatest common divisor
Pow${a}^{b}$ Power
PP$\mathbb{P}$ Prime numbers
ZZGreaterEqual$\mathbb{Z}_{\ge n}$ Integers greater than or equal to n
Source code for this entry:
Entry(ID("499cfc"),
Formula(Equal(GCD(Pow(p, m), Pow(q, n)), 1)),
Variables(p, q, m, n),
Assumptions(And(Element(p, PP), Element(q, PP), NotEqual(p, q), 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