Fungrim home page

Fungrim entry: 965ac0

{ax+by:xZ  and  yZ}={nd:nZ}   where d=gcd ⁣(a,b)\left\{ a x + b y : x \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; y \in \mathbb{Z} \right\} = \left\{ n d : n \in \mathbb{Z} \right\}\; \text{ where } d = \gcd\!\left(a, b\right)
Assumptions:aZ  and  bZa \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; b \in \mathbb{Z}
\left\{ a x + b y : x \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; y \in \mathbb{Z} \right\} = \left\{ n d : n \in \mathbb{Z} \right\}\; \text{ where } d = \gcd\!\left(a, b\right)

a \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; b \in \mathbb{Z}
Fungrim symbol Notation Short description
ZZZ\mathbb{Z} Integers
GCDgcd ⁣(a,b)\gcd\!\left(a, b\right) Greatest common divisor
Source code for this entry:
    Formula(Where(Equal(Set(Add(Mul(a, x), Mul(b, y)), For(Tuple(x, y)), And(Element(x, ZZ), Element(y, ZZ))), Set(Mul(n, d), ForElement(n, ZZ))), Equal(d, GCD(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