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Fungrim entry: 499cfc

gcd ⁣(pm,qn)=1\gcd\!\left({p}^{m}, {q}^{n}\right) = 1
Assumptions:pPandqPandpqandmZ0andnZ0p \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
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:
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), Unequal(p, q), Element(m, ZZGreaterEqual(0)), Element(n, ZZGreaterEqual(0)))))

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2019-08-17 11:32:46.829430 UTC