Fungrim home page

Fungrim entry: 126f3e

gcd ⁣(a,b)=d   where (d,u,v)=xgcd ⁣(a,b)\gcd\!\left(a, b\right) = d\; \text{ where } \left(d, u, v\right) = \operatorname{xgcd}\!\left(a, b\right)
Assumptions:aZandbZa \in \mathbb{Z} \,\mathbin{\operatorname{and}}\, b \in \mathbb{Z}
TeX:
\gcd\!\left(a, b\right) = d\; \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
GCDgcd ⁣(a,b)\gcd\!\left(a, b\right) Greatest common divisor
XGCDxgcd ⁣(a,b)\operatorname{xgcd}\!\left(a, b\right) Extended greatest common divisor
ZZZ\mathbb{Z} Integers
Source code for this entry:
Entry(ID("126f3e"),
    Formula(Equal(GCD(a, b), Where(d, 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.

2019-08-21 11:44:15.926409 UTC