Determine whether each of the following is true or false. Prove each true statement, and give a counterexample for each false statement. (a) There is an irreducible element of M6,10 that is a product of exactly 19 primes in Z. (b) No irreducible element of M1,6 is a product of exactly 4 primes in Z.

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Determine whether each of the following is true or false. Prove each true statement, and
give a counterexample for each false statement.
(a) There is an irreducible element of M6,10 that is a product of exactly 19 primes in Z.
(b) No irreducible element of M1,6 is a product of exactly 4 primes in Z.
Transcribed Image Text:Determine whether each of the following is true or false. Prove each true statement, and give a counterexample for each false statement. (a) There is an irreducible element of M6,10 that is a product of exactly 19 primes in Z. (b) No irreducible element of M1,6 is a product of exactly 4 primes in Z.
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