Important: The numtheory package has been deprecated.  Use the superseding command NumberTheory[QuadraticResidue] instead.

The function quadres will compute a generalized Legendre symbol $L\left(\frac{a}{b}\right)$ of a and b, which is defined to be 1 if a is a quadratic residue $\mathbf{mod}b$and -1 if a is a quadratic non-residue $\mathbf{mod}p$.  The number a is a quadratic residue mod b if it has a square root $\mathbf{mod}b$;  i.e., an integer c exists such that $c^2$ is congruent to $a\mathbf{mod}b$.

The command with(numtheory,quadres) allows the use of the abbreviated form of this command.

$\mathrm{with}\left(\mathrm{numtheory}\right)\:$

$\mathrm{quadres}\left(74\,101\right)$

$\mathrm{-1}$

$\mathrm{quadres}\left(0\,73\right)$

$1$

$\mathrm{quadres}\left(22\,11\right)$

$1$

$\mathrm{quadres}\left(5\,256\right)$

$\mathrm{-1}$

$\mathrm{quadres}\left(-2342\,1904\right)$

$\mathrm{-1}$