# 1105 as Sum of Two Squares

Jump to: navigation, search

## Theorem

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

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