`fmpz_mod_divides`

Synopsis#include <flint/fmpz_mod.h>

int fmpz_mod_divides(fmpz_t a, const fmpz_t b, const fmpz_t c, const fmpz_mod_ctx_t ctx)source

If the congruence $ac \equiv b \pmod n$ has a solution, sets $a$ to one solution in $[0, n)$ and returns 1; otherwise returns 0 and leaves $a$ undefined. $b$ and $c$ must be canonical.

With $g = \gcd(c, n) = xc + yn$ , a solution exists if and only if $g$ divides $b$ , and then $a = (b/g) x \bmod n$ is one; it is unique only if $g = 1$ . For $c = 0$ a solution exists only for $b = 0$ , and $a = 0$ is returned.

Guides#

Using fmpz_mod

Cite this page

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

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

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