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Fungrim entry: 8621f6

gcd ⁣(rs,c)=gcd ⁣(r,c)gcd ⁣(s,c)\gcd\!\left(r s, c\right) = \gcd\!\left(r, c\right) \gcd\!\left(s, c\right)
Assumptions:rZ  and  sZ  and  cZ  and  gcd ⁣(r,s)=1r \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; s \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; c \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; \gcd\!\left(r, s\right) = 1
\gcd\!\left(r s, c\right) = \gcd\!\left(r, c\right) \gcd\!\left(s, c\right)

r \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; s \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; c \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; \gcd\!\left(r, s\right) = 1
Fungrim symbol Notation Short description
GCDgcd ⁣(a,b)\gcd\!\left(a, b\right) Greatest common divisor
ZZZ\mathbb{Z} Integers
Source code for this entry:
    Formula(Equal(GCD(Mul(r, s), c), Mul(GCD(r, c), GCD(s, c)))),
    Variables(r, s, c),
    Assumptions(And(Element(r, ZZ), Element(s, ZZ), Element(c, ZZ), Equal(GCD(r, s), 1))))

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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