The answer to exercise marked [BB] can be found in the Back of the Book.Let A be the set o...

The answer to exercise marked [BB] can be found in the Back of the Book.

Let A be the set of congruence classes of integers modulo  some natural number n. For , define if ab ≡a2 (mod n). Prove or disprove that ≤ is a partial order in each of the following cases.

(a) n = p is a prime.

(b) n = pq is the product of two distinct primes.

(c) n is divisible by the square of a prime. [Hint. It might be helpful first to consider the case n = 12.]