Prove that no integer of the form 8k+7 can be expressed as the sum of three squares
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I have figured out a (long, and tedious) way to do it. But I was wondering if there is some sort of direct correlation or another path that I completely missed.
My attempt at the program was as follows:
A number of the form, 8k+7=7(mod8)8k+7=7(mod8). That is, we are looking for integers a, b, c such that a2+b2+c2=7(mod8)a2+b2+c2=7(mod8).
LONG and TEDIOUS way:
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