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) ? 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.

 

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