1105 as Sum of Two Squares
Theorem
$1105$ can be expressed as the sum of two squares in more ways than any smaller integer:
| \(\displaystyle 1105\) | \(=\) | \(\, \displaystyle 1089 + 16 \, \) | \(\, \displaystyle =\, \) | \(\displaystyle 33^2 + 4^2\) | $\quad$ | $\quad$ | |||||||
| \(\displaystyle \) | \(=\) | \(\, \displaystyle 1024 + 81 \, \) | \(\, \displaystyle =\, \) | \(\displaystyle 32^2 + 9^2\) | $\quad$ | $\quad$ | |||||||
| \(\displaystyle \) | \(=\) | \(\, \displaystyle 961 + 144 \, \) | \(\, \displaystyle =\, \) | \(\displaystyle 31^2 + 12^2\) | $\quad$ | $\quad$ | |||||||
| \(\displaystyle \) | \(=\) | \(\, \displaystyle 625 + 529 \, \) | \(\, \displaystyle =\, \) | \(\displaystyle 24^2 + 23^2\) | $\quad$ | $\quad$ |
Demonstrate there are no smaller with as many ways of doing this
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Sources
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $1105$
