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`	$\gcd\!\left(a, b\right)$	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(NotEqual(a, 0), NotEqual(b, 0)))))

Topics using this entry

Greatest common divisor