Fungrim entry: b43dac

\left|u\right| \le \frac{\left|b\right|}{d}\; \text{ where } \left(d, u, v\right) = \operatorname{xgcd}\!\left(a, b\right)

Assumptions:

a \in \mathbb{Z} \setminus \left\{0\right\} \,\mathbin{\operatorname{and}}\, b \in \mathbb{Z} \setminus \left\{0\right\}

TeX:

\left|u\right| \le \frac{\left|b\right|}{d}\; \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
`Abs`	$\left\|z\right\|$	Absolute value
`XGCD`	$\operatorname{xgcd}\!\left(a, b\right)$	Extended greatest common divisor
`ZZ`	$\mathbb{Z}$	Integers

Source code for this entry:

Entry(ID("b43dac"),
    Formula(Where(LessEqual(Abs(u), Div(Abs(b), d)), 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))))))

Topics using this entry

Greatest common divisor