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Fungrim entry: a9c81e

gcd ⁣(a,b)a\gcd\!\left(a, b\right) \mid a
Assumptions:aZandbZand(a0orb0)a \in \mathbb{Z} \,\mathbin{\operatorname{and}}\, b \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

a \in \mathbb{Z} \,\mathbin{\operatorname{and}}\, b \in \mathbb{Z} \,\mathbin{\operatorname{and}}\, \left(a \ne 0 \,\mathbin{\operatorname{or}}\, b \ne 0\right)
Definitions:
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:
Entry(ID("a9c81e"),
    Formula(Divides(GCD(a, b), a)),
    Variables(a, b),
    Assumptions(And(Element(a, ZZ), Element(b, ZZ), Or(Unequal(a, 0), Unequal(b, 0)))))

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Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2019-08-21 11:44:15.926409 UTC