# 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

- 1986: David Wells:
*Curious and Interesting Numbers*... (previous) ... (next): $1105$ - 1994: Richard K. Guy:
*Unsolved Problems in Number Theory*(2nd ed.) - 1997: David Wells:
*Curious and Interesting Numbers*(2nd ed.) ... (previous) ... (next): $1105$