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# Fungrim entry: fdae67

$\gcd\!\left({n}^{a} - 1, {n}^{b} - 1\right) = {n}^{\gcd\left(a, b\right)} - 1$
Assumptions:$a \in \mathbb{Z}_{\ge 0} \;\mathbin{\operatorname{and}}\; b \in \mathbb{Z}_{\ge 0} \;\mathbin{\operatorname{and}}\; n \in \mathbb{Z}_{\ge 1}$
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
GCD$\gcd\!\left(a, b\right)$ Greatest common divisor
Pow${a}^{b}$ Power
ZZGreaterEqual$\mathbb{Z}_{\ge n}$ 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)))))

## Topics using this entry

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2021-03-15 19:12:00.328586 UTC