What are the roots of x^(p-1) in Z_p?

Thread starter kathrynag
Start date Jan 9, 2011
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Polynomial Root

Jan 9, 2011

kathrynag

Let p be a prime number. Find all roots of x^(p-1) in Z_p

I have this definition.
Let f(x) be in F[x]. An element c in F is said to be a root of multiplicity m>=1 of f(x) if (x-c)^m|f(x), but (x-c)^(m+1) does not divide f(x).

I'm not sure if I use this idea somehow or not.

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Jan 9, 2011

eumyang

Homework Helper

I think Fermat's Little Theorem will be useful here.

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