The ModularSquareRoot function computes a non-negative integer $y$ such that $y^2=x\mathbf{mod}n$ if possible. If not possible, an error message is displayed.

When x has more than one square root, any one of them may be returned.

with(NumberTheory):

residues := {seq(i^2 mod 37, i = 0..36)};

$\mathrm{residues}≔\left\{0\,1\,3\,4\,7\,9\,10\,11\,12\,16\,21\,25\,26\,27\,28\,30\,33\,34\,36\right\}$

evalb(30 in residues);

$\mathrm{true}$

ModularSquareRoot(30, 37);

$17$

17^2 mod 37;

$30$

evalb(24 in residues);

$\mathrm{false}$

ModularSquareRoot(24, 37);

Error, (in NumberTheory:-ModularSquareRoot) 24 is a quadratic non-residue modulo 37

The NumberTheory[ModularSquareRoot] command was introduced in Maple 2016.

For more information on Maple 2016 changes, see Updates in Maple 2016.