# Fungrim entry: be5fcd

$\gcd\!\left(a, b\right) = d = a u + b v\; \text{ where } \left(d, u, v\right) = \operatorname{xgcd}\!\left(a, b\right)$
Assumptions:$a \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; b \in \mathbb{Z}$
TeX:
\gcd\!\left(a, b\right) = d = a u + b v\; \text{ where } \left(d, u, v\right) = \operatorname{xgcd}\!\left(a, b\right)

a \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; b \in \mathbb{Z}
Definitions:
Fungrim symbol Notation Short description
GCD$\gcd\!\left(a, b\right)$ Greatest common divisor
XGCD$\operatorname{xgcd}\!\left(a, b\right)$ Extended greatest common divisor
ZZ$\mathbb{Z}$ Integers
Source code for this entry:
Entry(ID("be5fcd"),
Formula(Where(Equal(GCD(a, b), d, Add(Mul(a, u), Mul(b, v))), Equal(Tuple(d, u, v), XGCD(a, b)))),
Variables(a, b),
Assumptions(And(Element(a, ZZ), Element(b, ZZ))))

## Topics using this entry

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

2021-03-15 19:12:00.328586 UTC