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Fungrim entry: fdae67

gcd⁡ ⁣(na−1,nb−1)=ngcd⁡(a,b)−1\gcd\!\left({n}^{a} - 1, {n}^{b} - 1\right) = {n}^{\gcd\left(a, b\right)} - 1
Assumptions:a∈Z≥0 and⁡ b∈Z≥0 and⁡ n∈Z≥1a \in \mathbb{Z}_{\ge 0} \,\mathbin{\operatorname{and}}\, b \in \mathbb{Z}_{\ge 0} \,\mathbin{\operatorname{and}}\, n \in \mathbb{Z}_{\ge 1}
TeX:
\gcd\!\left({n}^{a} - 1, {n}^{b} - 1\right) = {n}^{\gcd\left(a, b\right)} - 1

a \in \mathbb{Z}_{\ge 0} \,\mathbin{\operatorname{and}}\, b \in \mathbb{Z}_{\ge 0} \,\mathbin{\operatorname{and}}\, n \in \mathbb{Z}_{\ge 1}
Definitions:
Fungrim symbol Notation Short description
GCDgcd⁡ ⁣(n,k)\gcd\!\left(n, k\right) Greatest common divisor
Powab{a}^{b} Power
ZZGreaterEqualZ≥n\mathbb{Z}_{\ge n} Integers greater than or equal to n
Source code for this entry:
Entry(ID("fdae67"),
    Formula(Equal(GCD(Sub(Pow(n, a), 1), Sub(Pow(n, b), 1)), Sub(Pow(n, GCD(a, b)), 1))),
    Variables(a, b, n),
    Assumptions(And(Element(a, ZZGreaterEqual(0)), Element(b, ZZGreaterEqual(0)), Element(n, ZZGreaterEqual(1)))))

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2019-06-18 07:49:59.356594 UTC