Fungrim entry: 663d9c

\gcd\!\left(a, b\right) \mid a x + b y

Assumptions:

a \in \mathbb{Z} \,\mathbin{\operatorname{and}}\, b \in \mathbb{Z} \,\mathbin{\operatorname{and}}\, x \in \mathbb{Z} \,\mathbin{\operatorname{and}}\, y \in \mathbb{Z} \,\mathbin{\operatorname{and}}\, \left(a \ne 0 \,\mathbin{\operatorname{or}}\, b \ne 0\right)

TeX:

\gcd\!\left(a, b\right) \mid a x + b y

a \in \mathbb{Z} \,\mathbin{\operatorname{and}}\, b \in \mathbb{Z} \,\mathbin{\operatorname{and}}\, x \in \mathbb{Z} \,\mathbin{\operatorname{and}}\, y \in \mathbb{Z} \,\mathbin{\operatorname{and}}\, \left(a \ne 0 \,\mathbin{\operatorname{or}}\, b \ne 0\right)

Definitions:

Fungrim symbol	Notation	Short description
`GCD`	$\gcd\!\left(n, k\right)$	Greatest common divisor
`ZZ`	$\mathbb{Z}$	Integers

Source code for this entry:

Entry(ID("663d9c"),
    Formula(Divides(GCD(a, b), Add(Mul(a, x), Mul(b, y)))),
    Variables(a, b, x, y),
    Assumptions(And(Element(a, ZZ), Element(b, ZZ), Element(x, ZZ), Element(y, ZZ), Or(Unequal(a, 0), Unequal(b, 0)))))

Topics using this entry

Greatest common divisor