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.

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

$\mathrm{residues}≔\left\{\mathrm{seq}\left(i^3\mathbf{mod}24\,i=0..23\right)\right\}$

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

$\mathrm{evalb}\left(13\mathbf{in}\mathrm{residues}\right)$

$\mathrm{true}$

$\mathrm{ModularRoot}\left(13\,3\,24\right)$

$13$

${13}^3\mathbf{mod}24$

$13$

$\mathrm{evalb}\left(12\mathbf{in}\mathrm{residues}\right)$

$\mathrm{false}$

$\mathrm{ModularRoot}\left(12\,3\,24\right)$

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.