The SumOfSquares function computes the solutions to the sum of two squares problem.

The return value is a set $s$ of two-element lists of non-negative integers such that $\left[x\,y\right]$ is in $s$ if and only if $x\le y$ and $x^2+y^2=n$.

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

$\mathrm{SumOfSquares}\left(17\right)$

$\left\{\left[1\,4\right]\right\}$

$\mathrm{SumOfSquares}\left(938491\right)$

$\varnothing$

$s≔\mathrm{SumOfSquares}\left(10281960\right)$

$s≔\left\{\left[234\,3198\right]\,\left[1014\,3042\right]\,\left[1422\,2874\right]\,\left[1446\,2862\right]\,\left[2106\,2418\right]\right\}$

$\mathrm{map}\left(\mathrm{ss}\mapsto {\mathrm{ss}\left[1\right]}^2+{\mathrm{ss}\left[2\right]}^2\,s\right)$

$\left\{10281960\right\}$

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

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