Finding root of a polynomial

  1. 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.
     
  2. jcsd
  3. eumyang

    eumyang 1,347
    Homework Helper

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