Proving Finite Field Roots for Z_p

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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.
 
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You're being distracted by the ideal of polynomials; forget about them for a moment. What can you tell me about cp?
 
Ahh you're right! I was being distracted; all I need is Fermat's Little Theorem. Thanks a lot.
 

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