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Fungrim entry: 646745

gcd ⁣(ad,bd)=gcd ⁣(a,b)d\gcd\!\left(\frac{a}{d}, \frac{b}{d}\right) = \frac{\gcd\!\left(a, b\right)}{\left|d\right|}
Assumptions:aZ  and  bZ  and  dZ  and  da  and  dba \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; b \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; d \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; d \mid a \;\mathbin{\operatorname{and}}\; d \mid b
\gcd\!\left(\frac{a}{d}, \frac{b}{d}\right) = \frac{\gcd\!\left(a, b\right)}{\left|d\right|}

a \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; b \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; d \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; d \mid a \;\mathbin{\operatorname{and}}\; d \mid b
Fungrim symbol Notation Short description
GCDgcd ⁣(a,b)\gcd\!\left(a, b\right) Greatest common divisor
Absz\left|z\right| Absolute value
ZZZ\mathbb{Z} Integers
Source code for this entry:
    Formula(Equal(GCD(Div(a, d), Div(b, d)), Div(GCD(a, b), Abs(d)))),
    Variables(a, b, d),
    Assumptions(And(Element(a, ZZ), Element(b, ZZ), Element(d, ZZ), Divides(d, a), Divides(d, b))))

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2021-03-15 19:12:00.328586 UTC