I have been struggling with this can someone help Please?

a.Prove that if a polynomial is irreducible in Z_p[x], then it

is irreducible in Z[x].

b.Prove that if a polynomial factors in Z[x], then it factors in

Z_p[x] for some prime p.

Thank u!

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- May 26th 2010, 08:11 PM #1

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- May 27th 2010, 01:24 AM #2

- May 27th 2010, 05:01 AM #3

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- May 27th 2010, 06:10 AM #4
Personally, I would do question (b), then extend it for all primes p. This is the contrapositive of (a)*, so you are done.

That is a bit roundabout though, so there may be an easier way...

*The contrapositive: Instead of proving $\displaystyle A \Rightarrow B$ you prove $\displaystyle not B \Rightarrow not A$. These two things are equivalent.