How is this done?

**twittytwitter** · March 11th, 2010, 03:28 PM

Find a polynomial of positive degree in Z9[x] that is a unit.

I'm a bit confused here, I know a unit is an element a such that au=1=ua, but I don't know how to find a polynomial of that form here. Any ideas? Thanks.

And just one more general question...Do we consider something like just x^2 to be irreducible, in say, Z2[x] or not since it can be written x*x?

**hatsoff** · March 11th, 2010, 05:22 PM

Originally Posted by twittytwitter

Find a polynomial of positive degree in Z9[x] that is a unit.

I'm a bit confused here, I know a unit is an element a such that au=1=ua, but I don't know how to find a polynomial of that form here. Any ideas? Thanks.

EDIT: $(1-3x)(1+3x)=1-9x^2\cong 1\pmod{9}$ . So $1-3x$ and $1+3x$ are units.

And just one more general question...Do we consider something like just x^2 to be irreducible, in say, Z2[x] or not since it can be written x*x?

Yes.

**twittytwitter** · March 11th, 2010, 07:06 PM

Thanks, sounds good.

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