Fungrim home page

Fungrim entry: 5aad5c

gcd ⁣(rm,sn)=1\gcd\!\left({r}^{m}, {s}^{n}\right) = 1
Assumptions:rZandsZandgcd ⁣(r,s)=1andmZ0andnZ0r \in \mathbb{Z} \,\mathbin{\operatorname{and}}\, s \in \mathbb{Z} \,\mathbin{\operatorname{and}}\, \gcd\!\left(r, s\right) = 1 \,\mathbin{\operatorname{and}}\, m \in \mathbb{Z}_{\ge 0} \,\mathbin{\operatorname{and}}\, n \in \mathbb{Z}_{\ge 0}
TeX:
\gcd\!\left({r}^{m}, {s}^{n}\right) = 1

r \in \mathbb{Z} \,\mathbin{\operatorname{and}}\, s \in \mathbb{Z} \,\mathbin{\operatorname{and}}\, \gcd\!\left(r, s\right) = 1 \,\mathbin{\operatorname{and}}\, m \in \mathbb{Z}_{\ge 0} \,\mathbin{\operatorname{and}}\, n \in \mathbb{Z}_{\ge 0}
Definitions:
Fungrim symbol Notation Short description
GCDgcd ⁣(a,b)\gcd\!\left(a, b\right) Greatest common divisor
Powab{a}^{b} Power
ZZZ\mathbb{Z} Integers
ZZGreaterEqualZn\mathbb{Z}_{\ge n} Integers greater than or equal to n
Source code for this entry:
Entry(ID("5aad5c"),
    Formula(Equal(GCD(Pow(r, m), Pow(s, n)), 1)),
    Variables(r, s, m, n),
    Assumptions(And(Element(r, ZZ), Element(s, ZZ), Equal(GCD(r, s), 1), 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.

2019-08-19 14:38:23.809000 UTC