The RootsOfUnity(k, n) command computes all the kth roots of unity modulo n.

An integer $x$ is said to be a $k$th root of unity modulo $n$ if $x^k=1\mathbf{mod}n$.

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

$\mathrm{unity}≔\mathrm{RootsOfUnity}\left(5\,8965\right)$

$\mathrm{unity}≔\left\{1\,1631\,2446\,3261\,6521\right\}$

$\mathrm{map}\left(x\mapsto x^5\mathbf{mod}8965\,\mathrm{unity}\right)$

$\left\{1\right\}$

$\mathrm{plots}:-\mathrm{pointplot}\left(\mathrm{select}\left(p\mapsto {p\left[2\right]}^2\mathbf{mod}p\left[1\right]=1\,\left[\mathrm{seq}\left(\mathrm{seq}\left(\left[i\,j\right]\,j=0..i-1\right)\,i=1..1000\right)\right]\right)\,\mathrm{labels}=\left[''Modulus''\,''Second\; roots\; of\; unity''\right]\,\mathrm{labeldirections}=\left[\mathrm{horizontal}\,\mathrm{vertical}\right]\right)$

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

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