How could I put them as two true squares (side at least 2) ? Solution

as three squares ? Solution

as 4 squares ? Solution

Along with 65 =8²+1² these are the only ways of writing 65 as a sum of squares.

(of **at most 4** squares, for instance 65 = 1² + 1² + ... + 1² with 65 terms is uninteresting !)

And also "sum of square" reminds you what ?

Smallest hypothenuse common to at least 10 different right triangles with integer sides.

Solution

On an A4 (210×297) sheet of 5mm×5mms squared paper, find the circle centered on the grid
and going at the maximum number of points on the grid.

Solution

Methods and proofs

Script for decomposition of N as sum of two squares.