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Fungrim entry: 07ac4a

gcd ⁣(a+nb,b)=gcd ⁣(a,b)\gcd\!\left(a + n b, b\right) = \gcd\!\left(a, b\right)
Assumptions:aZandbZandnZa \in \mathbb{Z} \,\mathbin{\operatorname{and}}\, b \in \mathbb{Z} \,\mathbin{\operatorname{and}}\, n \in \mathbb{Z}
TeX:
\gcd\!\left(a + n b, b\right) = \gcd\!\left(a, b\right)

a \in \mathbb{Z} \,\mathbin{\operatorname{and}}\, b \in \mathbb{Z} \,\mathbin{\operatorname{and}}\, n \in \mathbb{Z}
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("07ac4a"),
    Formula(Equal(GCD(Add(a, Mul(n, b)), b), GCD(a, b))),
    Variables(a, b, n),
    Assumptions(And(Element(a, ZZ), Element(b, ZZ), Element(n, ZZ))))

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

2019-10-05 13:11:19.856591 UTC