Proving Finite Field Roots for Z_p

jeffreydk · Apr 26, 2009

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 · Apr 26, 2009

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

jeffreydk · Apr 26, 2009

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

Proving Finite Field Roots for Z_p

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