Sum of 2 Squares in 3 Distinct Ways

Theorem

The following positive integers can be expressed as the sum of $2$ square numbers in $3$ distinct ways:

$325, 425, 650, 725, 845, 850, 925, 1025, 1105, 1250, \dots$

This sequence is A025294 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).

Examples

$325$ as the Sum of 3 Squares

$325$ is the smallest positive integer which can be expressed as the sum of two square numbers in three distinct ways:

\(\ds 325\)

\(=\)

\(\ds 18^2 + 1^2\)

\(\ds \)

\(=\)

\(\ds 17^2 + 6^2\)

\(\ds \)

\(=\)

\(\ds 15^2 + 10^2\)