Proving Finite Field Roots for Z_p

[jeffreydk]

I am trying to prove that if c is a root of f(x) in Z_p then c^p is also a root. It seems very simple but I can't think how to approach it. Any insight on this would be greatly appreciated, and sorry for not using the latex but it seems to be acting up.

 

[Hurkyl]

You're being distracted by the ideal of polynomials; forget about them for a moment. What can you tell me about c^p?

 

[jeffreydk]

Ahh you're right! I was being distracted; all I need is Fermat's Little Theorem. Thanks a lot.