# 1105 as Sum of Two Squares

## 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

- 1997: David Wells:
*Curious and Interesting Numbers*(2nd ed.) ... (previous) ... (next): $1105$