Ciro Santilli @cirosantilli 37

And when it can't, attempt to classify which subset of the integers can be reached. E.g. Legendre's three-square theorem.

4 squares are sufficient by Lagrange's four-square theorem.

3 is not enough by Legendre's three-square theorem.

The subsets reachable with 2 and 3 squares are fully characterized by Legendre's three-square theorem.