Fungrim entry: 5aad5c

\gcd\!\left({r}^{m}, {s}^{n}\right) = 1

Assumptions:

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}

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
`GCD`	$\gcd\!\left(a, b\right)$	Greatest common divisor
`Pow`	${a}^{b}$	Power
`ZZ`	$\mathbb{Z}$	Integers
`ZZGreaterEqual`	$\mathbb{Z}_{\ge n}$	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

Greatest common divisor