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Fungrim entry: 959a25

gcd⁡ ⁣(a mod b,b)=gcd⁡ ⁣(a,b)\gcd\!\left(a \bmod b, b\right) = \gcd\!\left(a, b\right)
Assumptions:a∈Z and⁡ b∈Z and⁡ b≠0a \in \mathbb{Z} \,\mathbin{\operatorname{and}}\, b \in \mathbb{Z} \,\mathbin{\operatorname{and}}\, b \ne 0
TeX:
\gcd\!\left(a \bmod b, b\right) = \gcd\!\left(a, b\right)

a \in \mathbb{Z} \,\mathbin{\operatorname{and}}\, b \in \mathbb{Z} \,\mathbin{\operatorname{and}}\, b \ne 0
Definitions:
Fungrim symbol Notation Short description
GCDgcd⁡ ⁣(n,k)\gcd\!\left(n, k\right) Greatest common divisor
ZZZ\mathbb{Z} Integers
Source code for this entry:
Entry(ID("959a25"),
    Formula(Equal(GCD(Mod(a, b), b), GCD(a, b))),
    Variables(a, b),
    Assumptions(And(Element(a, ZZ), Element(b, ZZ), 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.

2019-06-18 07:49:59.356594 UTC