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

Greatest common divisor

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