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Fungrim entry: da7d00

(abandb2d)    (2du<b)   where (d,u,v)=xgcd ⁣(a,b)\left(\left|a\right| \ne \left|b\right| \,\mathbin{\operatorname{and}}\, \left|b\right| \ne \left|2 d\right|\right) \implies \left(2 d \left|u\right| < \left|b\right|\right)\; \text{ where } \left(d, u, v\right) = \operatorname{xgcd}\!\left(a, b\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:
\left(\left|a\right| \ne \left|b\right| \,\mathbin{\operatorname{and}}\, \left|b\right| \ne \left|2 d\right|\right) \implies \left(2 d \left|u\right| < \left|b\right|\right)\; \text{ where } \left(d, u, v\right) = \operatorname{xgcd}\!\left(a, b\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
Absz\left|z\right| Absolute value
XGCDxgcd ⁣(a,b)\operatorname{xgcd}\!\left(a, b\right) Extended greatest common divisor
ZZZ\mathbb{Z} Integers
Source code for this entry:
Entry(ID("da7d00"),
    Formula(Where(Implies(And(Unequal(Abs(a), Abs(b)), Unequal(Abs(b), Abs(Mul(2, d)))), Less(Mul(Mul(2, d), Abs(u)), Abs(b))), Equal(Tuple(d, u, v), XGCD(a, 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