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Fungrim entry: 663d9c

gcd ⁣(a,b)ax+by\gcd\!\left(a, b\right) \mid a x + b y
Assumptions:aZandbZandxZandyZand(a0orb0)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)
\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)
Fungrim symbol Notation Short description
GCDgcd ⁣(a,b)\gcd\!\left(a, b\right) Greatest common divisor
ZZZ\mathbb{Z} Integers
Source code for this entry:
    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)))))

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2019-10-05 13:11:19.856591 UTC