a) Let a be an integer What values can a 2 take on, mod 8 b) Prove that, when a, b, and c are integers, it's impossible that a 2 b 2 c 2 is congruent to 7 (mod 8) (Thus, there exist infinitely many positive integers that cannot be written as sums of three squares )

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Question: a) Let a be an integer. What values can a 2 take on, mod 8? b) Prove that, when a, b, and c are integers,

a) Let a be an integer. What values can a²take on, mod 8?

b) Prove that, when a, b, and c are integers, it's impossible that a²+ b²+ c²is congruent to 7 (mod 8). (Thus, there exist infinitely many positive integers that cannot be written as sums of three squares.)

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