Fungrim entry: 499cfc

\gcd\!\left({p}^{m}, {q}^{n}\right) = 1

Assumptions:

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}

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
`GCD`	$\gcd\!\left(a, b\right)$	Greatest common divisor
`Pow`	${a}^{b}$	Power
`PP`	$\mathbb{P}$	Prime numbers
`ZZGreaterEqual`	$\mathbb{Z}_{\ge n}$	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), NotEqual(p, q), Element(m, ZZGreaterEqual(0)), Element(n, ZZGreaterEqual(0)))))

Topics using this entry

Greatest common divisor