How to factor a polynomial modulo p?

  1. I can understand most of Galois Theory and Number Theory dealing with factorization and extension fields, but I always run into problems that involve factorization mod p, which I can't seem to figure out how to do. I can't find any notes anywhere either, so I was wondering if someone could give me some steps. p is prime, of course.
  2. jcsd
  3. morphism

    morphism 2,020
    Science Advisor
    Homework Helper

    Do you have any specific questions? For general reading material, you could try googling "factoring polynomials over finite fields".
  4. I seem to have figured out how to factor mod p (in a prime field) between a couple documents:

    However, I'm still wondering what other types of finite fields it would be useful to factor over (am I correct in assuming that not all finite fields are prime fields?)
  5. You usually reduce the polynomial using the small Fermat theorem, xp [itex]\equiv[/itex] x (mod p) for every variable x that has a power greater than p-1
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