1. Let p be a prime and let g be a primitive root modulo p. Let a be an integer which is relatively prime to p. Prove that a has a square root modulo p (i.e., there exists an integer b such that b² = a (mod p)) if and only if the discrete logarithm log, (a) is even.

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A: Note that : Since you have posted multiple questions, we will provide the solution only to the first…

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