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Fungrim entry: 6880d0

gcd ⁣(a,b)=max{d:dZ1anddaanddb}\gcd\!\left(a, b\right) = \max \left\{ d : d \in \mathbb{Z}_{\ge 1} \,\mathbin{\operatorname{and}}\, d \mid a \,\mathbin{\operatorname{and}}\, d \mid b \right\}
Assumptions:aZandbZand(a0orb0)a \in \mathbb{Z} \,\mathbin{\operatorname{and}}\, b \in \mathbb{Z} \,\mathbin{\operatorname{and}}\, \left(a \ne 0 \,\mathbin{\operatorname{or}}\, b \ne 0\right)
\gcd\!\left(a, b\right) = \max \left\{ d : d \in \mathbb{Z}_{\ge 1} \,\mathbin{\operatorname{and}}\, d \mid a \,\mathbin{\operatorname{and}}\, d \mid b \right\}

a \in \mathbb{Z} \,\mathbin{\operatorname{and}}\, b \in \mathbb{Z} \,\mathbin{\operatorname{and}}\, \left(a \ne 0 \,\mathbin{\operatorname{or}}\, b \ne 0\right)
Fungrim symbol Notation Short description
GCDgcd ⁣(a,b)\gcd\!\left(a, b\right) Greatest common divisor
MaximummaxxSf(x)\mathop{\max}\limits_{x \in S} f(x) Maximum value of a set or function
ZZGreaterEqualZn\mathbb{Z}_{\ge n} Integers greater than or equal to n
ZZZ\mathbb{Z} Integers
Source code for this entry:
    Formula(Equal(GCD(a, b), Maximum(Set(d, For(d), And(Element(d, ZZGreaterEqual(1)), Divides(d, a), Divides(d, b)))))),
    Variables(a, b),
    Assumptions(And(Element(a, ZZ), Element(b, ZZ), Or(Unequal(a, 0), Unequal(b, 0)))))

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Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2019-10-05 13:11:19.856591 UTC