1105 as Sum of Two Squares

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Theorem

$1105$ can be expressed as the sum of two squares in more ways than any smaller integer:

\(\ds 1105\) \(=\) \(\, \ds 1089 + 16 \, \) \(\, \ds = \, \) \(\ds 33^2 + 4^2\)
\(\ds \) \(=\) \(\, \ds 1024 + 81 \, \) \(\, \ds = \, \) \(\ds 32^2 + 9^2\)
\(\ds \) \(=\) \(\, \ds 961 + 144 \, \) \(\, \ds = \, \) \(\ds 31^2 + 12^2\)
\(\ds \) \(=\) \(\, \ds 625 + 529 \, \) \(\, \ds = \, \) \(\ds 24^2 + 23^2\)


Proof


Sources