Sum of one, two, and three squares If a square $n^2$ can be written as the sum of two nonzero squares as well as the sum of three nonzero squares, then can we conclude that it can be written as the sum of any number of nonzero squares up to $n^2 - 14$ nonzero squares?
Example: $13^2 = 12^2 + 5^2 = 12^2 + 4^2 + 3^2$. But also $13^2 = 11^2 + 4^2 + 4^2 + 4^2$ and $13^2 = 12^2 + 4^2 + 2^2 + 2^2 + 1^2$ etc up to $13^2 = 3^2 + 2^2 + 2^2 + 1^2 + .. + 1^2$. 

Yes, because all numbers can be written as the sum of four squares.
