Important: The numtheory package has been deprecated.  Use the superseding command NumberTheory[SumOfSquares] instead.

The sum2sqr returns the solutions of the sum of two squares problem.

The result is returned as in the form $\&lsqb;\&lsqb;a_1,b_1\&rsqb;,\&lsqb;a_2,b_2\&rsqb;,\mathrm{...},\&lsqb;a_n,b_n\&rsqb;$ where $a_i$, $b_i$ are non-negative integers, $a_i^2+b_i^2=n$, and $a_i<=b_i,1<=i<=n$.

The command with(numtheory,sum2sqr) allows the use of the abbreviated form of this command.

$\mathrm{with}\left(\mathrm{numtheory}\right)\&colon;$

$\mathrm{sum2sqr}\left(17\right)$

$\left[\left[1\&comma;4\right]\right]$

$\mathrm{sum2sqr}\left(938491\right)$

$\mathrm{sum2sqr}\left(10281960\right)$

$\left[\left[234\&comma;3198\right]\&comma;\left[1014\&comma;3042\right]\&comma;\left[1422\&comma;2874\right]\&comma;\left[1446\&comma;2862\right]\&comma;\left[2106\&comma;2418\right]\right]$