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NumberTheory

 SumOfSquares
 solutions to the sum of two squares problem

 Calling Sequence SumOfSquares(n)

Parameters

 n - integer

Description

 • 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 ${x}^{2}+{y}^{2}=n$.

Examples

 > $\mathrm{with}\left(\mathrm{NumberTheory}\right):$
 > $\mathrm{SumOfSquares}\left(17\right)$
 $\left\{\left[{1}{,}{4}\right]\right\}$ (1)
 > $\mathrm{SumOfSquares}\left(938491\right)$
 ${\varnothing }$ (2)
 > $s≔\mathrm{SumOfSquares}\left(10281960\right)$
 ${s}{≔}\left\{\left[{234}{,}{3198}\right]{,}\left[{1014}{,}{3042}\right]{,}\left[{1422}{,}{2874}\right]{,}\left[{1446}{,}{2862}\right]{,}\left[{2106}{,}{2418}\right]\right\}$ (3)
 > $\mathrm{map}\left(\mathrm{ss}→{\mathrm{ss}}_{1}^{2}+{\mathrm{ss}}_{2}^{2},s\right)$
 $\left\{{10281960}\right\}$ (4)

Compatibility

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