Question: a) Prove that if p = 4n + 3 is a prime, and y = x? (mod p) is a non-zero residue, then p+1

a) Prove that if p = 4n + 3 is a prime,

a) Prove that if p = 4n + 3 is a prime, and y = x? (mod p) is a non-zero residue, then p+1 x = ty (mod p). b) Determine whether or not x? = 85 (mod 97) has a solution.

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