# Ideals and Factor Rings : Annihilators

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If R is a commutative ring, a polynomial f(x) in R[x] is said to annihilate R if f(a) = 0 for every a belonging to R

Show that x^p - x annihilates Zp (Z is integers).

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#### Solution Preview

Proof:

By Fermat's theorem, if p is a prime, then x^(p-1)=1 (mod p) for any x in Zp. So ...

#### Solution Summary

An annihilator is identified and Fermat's theorem is used.

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