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GaussInt

 GIquadres
 quadratic residue and non-residue

 Calling Sequence GIquadres(a, b)

Parameters

 a, b - Gaussian integers

Description

 • The function GIquadres returns $1$ if a is a quadratic residue $\mathbf{mod}b$, and $-1$ if a is a quadratic non-residue $\mathbf{mod}b$.
 • The number a is a quadratic residue of b where a and b are coprime if a has a square root $\mathbf{mod}b$, that is, there exists a Gaussian integer c such that ${c}^{2}$ is congruent to $a\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}\mathbf{mod}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}b$.

Examples

 > $\mathrm{with}\left(\mathrm{GaussInt}\right):$
 > $\mathrm{GIquadres}\left(-1,3+7I\right)$
 ${1}$ (1)
 > $\mathrm{GIquadres}\left(47364374-48434834I,84734834-3434347I\right)$
 ${-}{1}$ (2)

 See Also