FLINT3.7.0-dev
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_aprcl_is_gausspower_2q_equal_first, _aprcl_is_gausspower_2q_equal_second, _aprcl_is_gausspower_from_unity_p

Synopsis#include <flint/aprcl.h>
int _aprcl_is_gausspower_2q_equal_first(ulong q, const fmpz_t n)source
int _aprcl_is_gausspower_2q_equal_second(ulong q, const fmpz_t n)source
slong _aprcl_is_gausspower_from_unity_p(ulong q, ulong r, const fmpz_t n)source

Checks of the Gauss sum test, for the Gauss sum τ(χ)\tau(\chi) of a character χ\chi of conductor qq: whether (χ(−1)q)(n−1)/2≡−1(modn)(\chi(-1) q)^{(n-1)/2} \equiv -1 \pmod n and whether q(n−1)/2≡−1(modn)q^{(n-1)/2} \equiv -1 \pmod n (for the quadratic character, returning 1 or 0), and for a character of order rr, returns ii such that τ(χn)=ζriτ(χ)n\tau(\chi^n) = \zeta_r^i \tau(\chi)^n, or −1-1 if there is none.

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The FLINT team, “_aprcl_is_gausspower_2q_equal_first, _aprcl_is_gausspower_2q_equal_second, _aprcl_is_gausspower_from_unity_p (aprcl.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/aprcl/_aprcl_is_gausspower_2q_equal_first.html (generated 2026-11-02).