CongruentMod

Whether $a \equiv b \pmod m$ -- true exactly when $m \mid (a - b)$.

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CongruentMod(a, b, m) -> booleanexact for arbitrary-precision integers, past double precision

Typed signatures

Type	Package	Applies
(integer, integer, integer) -> boolean	analytic	always

Domain: Number theory

Examples

Basic #

$5 \equiv 2 \pmod 3$ since $3 \mid (5-2)$

live ↗

In$\mathrm{CongruentMod}(5, 2, 3)$Out$\mathrm{True}$

Scope #

live ↗

In$\mathrm{CongruentMod}(5, 1, 3)$Out$\mathrm{False}$

A value is always congruent to itself, mod anything

live ↗

In$\mathrm{CongruentMod}(7, 7, 5)$Out$\mathrm{True}$

live ↗

In$\mathrm{CongruentMod}(7, 1, 3)$Out$\mathrm{True}$

Exact for arbitrary-precision integers, past double precision

live ↗

In$\mathrm{CongruentMod}(12\,345\,678\,901\,234\,567\,891, 2, 7)$Out$\mathrm{True}$

live ↗

In$\mathrm{CongruentMod}(12\,345\,678\,901\,234\,567\,891, 3, 7)$Out$\mathrm{False}$

About

Examples	6
Crosswalk	FungrimFungrim entry ×7

See also: Mod, GCD