Fungrim home page

Fungrim entry: 499cfc

gcd ⁣(pm,qn)=1\gcd\!\left({p}^{m}, {q}^{n}\right) = 1
Assumptions:pP  and  qP  and  pq  and  mZ0  and  nZ0p \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}
\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}
Fungrim symbol Notation Short description
GCDgcd ⁣(a,b)\gcd\!\left(a, b\right) Greatest common divisor
Powab{a}^{b} Power
PPP\mathbb{P} Prime numbers
ZZGreaterEqualZn\mathbb{Z}_{\ge n} Integers greater than or equal to n
Source code for this entry:
    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