Prove that for every prime p, the polynomial x^p-x-1 is irreducible over Z_p
Don't even know where to start, can you please help me?
A non-constant polynomial (where is a field, like ) is irreducible iff we cannot write where i.e. factorize into lower degree polynomials.
If is irreducible then has no zeros in . But the converse is not true. Consider . Certainly has no zeros in . However, . Thus, is reducible.
Does that make sense?