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Fungrim entry: be5fcd

gcd ⁣(a,b)=d=au+bv   where (d,u,v)=xgcd ⁣(a,b)\gcd\!\left(a, b\right) = d = a u + b v\; \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 = 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
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("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

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2019-10-05 13:11:19.856591 UTC