# Fungrim entry: 5daceb

Symbol: XGCD $\operatorname{xgcd}\!\left(a, b\right)$ Extended greatest common divisor
Domain Codomain
$a \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; b \in \mathbb{Z}$ $d \in \mathbb{Z}_{\ge 0} \;\mathbin{\operatorname{and}}\; u \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; v \in \mathbb{Z}\; \text{ where } \left(d, u, v\right) = \operatorname{xgcd}\!\left(a, b\right)$
Table data: $\left(P, Q\right)$ such that $\left(P\right) \;\implies\; \left(Q\right)$
Definitions:
Fungrim symbol Notation Short description
XGCD$\operatorname{xgcd}\!\left(a, b\right)$ Extended greatest common divisor
ZZ$\mathbb{Z}$ Integers
ZZGreaterEqual$\mathbb{Z}_{\ge n}$ Integers greater than or equal to n
Source code for this entry:
Entry(ID("5daceb"),
SymbolDefinition(XGCD, XGCD(a, b), "Extended greatest common divisor"),
Table(TableRelation(Tuple(P, Q), Implies(P, Q)), TableHeadings(Description("Domain"), Description("Codomain")), List(Tuple(And(Element(a, ZZ), Element(b, ZZ)), Where(And(Element(d, ZZGreaterEqual(0)), Element(u, ZZ), Element(v, ZZ)), Equal(Tuple(d, u, v), XGCD(a, b)))))))

## 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