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Fungrim entry: 5aad5c

gcd ⁣(rm,sn)=1\gcd\!\left({r}^{m}, {s}^{n}\right) = 1
Assumptions:rZ  and  sZ  and  gcd ⁣(r,s)=1  and  mZ0  and  nZ0r \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}
\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}
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:
    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)))))

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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