`nmod_divides`

Synopsis#include <flint/nmod.h>

int nmod_divides(ulong * a, ulong b, ulong c, nmod_t mod)source

If $ac \equiv b \pmod n$ has a solution, sets *a to one solution and returns 1; otherwise returns 0. Unlike nmod_div, this works when $c$ is not invertible. Requires reduced $b$ and $c$ .

The congruence $ac \equiv b \pmod n$ is solvable if and only if $g = \gcd(c, n)$ divides $b$ , and then it has exactly $g$ solutions modulo $n$ . nmod_divides computes $u$ with $u c \equiv g \pmod n$ by the extended Euclidean algorithm and returns $a = (b/g)\, u \bmod n$ , which is not necessarily the least solution. If $c = 0$ , then *a is set to 0, and the return value is 1 if $b = 0$ and 0 otherwise. When there is no solution and $c \ne 0$ , *a is not modified.

Guides#

Cite this page

The FLINT team, “nmod_divides (nmod.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/nmod/nmod_divides.html (generated 2026-11-02).

@misc{flint-doc-nmod-nmod-divides,
  author       = {{The FLINT team}},
  title        = {{nmod\_divides (nmod.h)}},
  howpublished = {FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev},
  year         = {2026},
  url          = {https://flintlib.org/doc/nmod/nmod_divides.html},
  note         = {Generated 2026-11-02}
}

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