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

When x has more than one roots of order r, any one of them may be returned.

with(NumberTheory):

residues := {seq(i^3 mod 24, i = 0..23)};

$\mathrm{residues}≔\left\{0\,1\,3\,5\,7\,8\,9\,11\,13\,15\,16\,17\,19\,21\,23\right\}$

evalb(13 in residues);

$\mathrm{true}$

ModularRoot(13, 3, 24);

$13$

13^3 mod 24;

$13$

evalb(12 in residues);

$\mathrm{false}$

ModularRoot(12, 3, 24);

Error, (in NumberTheory:-ModularRoot) 12 is a 3rd order non-residue modulo 24

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

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