Let p be a prime divisor of a positive integer n. Prove
Chapter 18, Problem 30E(choose chapter or problem)
Let p be a prime divisor of a positive integer n. Prove that p is irreducible in \(Z_n\) if and only if \(p^2\) divides n. (See Exercise 28).
Exercise 28
For a commutative ring with unity we may define associates, irreducibles, and primes exactly as we did for integral domains. With these definitions, show that both 2 and 3 are prime in \(Z_{12}\) but 2 is irreducible and 3 is not.
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