Find the number of triples (a, b, c) of positive integers, such that 1 <= a ,b, c <= 100 and a^2 + b^2 + c^2 = 100.
No three positive integers work here
Supplementary question.
Triples exist for sums of 30, 50, 70, and 90, but not for 20, 40, 60, 80 and 100.
Explain why this is so.