Sum of squares
I have 65 marbles that I can put in a 5×13 rectangle.
How could I put them as two true squares (side at least 2) ?
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.
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.
Methods and proofs
Script for decomposition of N as sum of two squares.