Let p be an odd prime and a be any integer which is not congruent to...

Let p be an odd prime and a be any integer which is not congruent to 0 modulo p.

Prove that the congruence x 2 ≡ −a 2 (mod p) has solutions if and only if p ≡ 1 (mod 4).

Hint: Naturally, you may build your proof on the fact that the statement to be proved is valid for the case a = 1.

Expert Solution

Colby Messinger answered 2 years ago

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Let p be an odd prime and a be any integer which is not congruent to...

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