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Fungrim entry: f91d1c

gcd ⁣(a,b)min ⁣(a,b)\gcd\!\left(a, b\right) \le \min\!\left(\left|a\right|, \left|b\right|\right)
Assumptions:aZ{0}andbZ{0}a \in \mathbb{Z} \setminus \left\{0\right\} \,\mathbin{\operatorname{and}}\, b \in \mathbb{Z} \setminus \left\{0\right\}
TeX:
\gcd\!\left(a, b\right) \le \min\!\left(\left|a\right|, \left|b\right|\right)

a \in \mathbb{Z} \setminus \left\{0\right\} \,\mathbin{\operatorname{and}}\, b \in \mathbb{Z} \setminus \left\{0\right\}
Definitions:
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:
Entry(ID("f91d1c"),
    Formula(LessEqual(GCD(a, b), Min(Abs(a), Abs(b)))),
    Variables(a, b),
    Assumptions(And(Element(a, SetMinus(ZZ, Set(0))), Element(b, SetMinus(ZZ, Set(0))))))

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2019-09-19 20:12:49.583742 UTC