Question: (a) If z is a Gaussian integer and its norm N(z) is a prime in Z , prove that z is a Gaussian prime. (b)

(a) If z is a Gaussian integer and its norm N(z) is a prime in Z , prove that z is a Gaussian

prime.

(b) Prove that 7 + 2i is a Gaussian prime.

(c) Factor 109 into Gaussian primes, and explain why your answer is correct.

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