Fungrim home page

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)
TeX:
\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)
Definitions:
Fungrim symbol Notation Short description
GCDgcd ⁣(a,b)\gcd\!\left(a, b\right) Greatest common divisor
MaximummaxP(x)f ⁣(x)\mathop{\max}\limits_{P\left(x\right)} f\!\left(x\right) Maximum value of a set or function
SetBuilder{f ⁣(x):P ⁣(x)}\left\{ f\!\left(x\right) : P\!\left(x\right) \right\} Set comprehension
ZZGreaterEqualZn\mathbb{Z}_{\ge n} Integers greater than or equal to n
ZZZ\mathbb{Z} Integers
Source code for this entry:
Entry(ID("6880d0"),
    Formula(Equal(GCD(a, b), Maximum(SetBuilder(d, 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)))))

Topics using this entry

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

2019-08-21 11:44:15.926409 UTC