On Jun 7, 4:10 pm, Saysero <says...@gmail.com> wrote:
> Is there m in M such that for all n in N if n>m then: > 1) there exist k and x_1,...,x_n in N so that n=(x_1)^2 + ... + > (x_k)^2 and > 2) (i != j) => (x_j != x_i) > The question is, simply put, can every number greater than some m be > represented as a sum of unique squares. > I hope this makes my question better understood.
A better way to say this is "distinct" instead of "unique". The answer is yes, and m=128 is the largest exceptional value. I worked this out by hand in 1995. It's not hard. But for much more detail, see http://mathworld.wolfram.com/SquareNumber.html