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:


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



Sources