1. Let n be a natural number with n > 1. (a) Suppose n is prime. Prove that if ab = 0 (mod n), then a = 0 (mod n) or b = 0 (mod n). (b) Is the implication in (a) still true if n is composite? Justify your answer.

1. Let n be a natural number with n > 1. (a) Suppose n is prime. Prove that if ab = 0 (mod n), then a = 0 (mod n) or b = 0 (mod n). (b) Is the implication in (a) still true if n is composite? Justify your answer.

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