Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Solving Polynimals in the ring mod p^r

  1. Oct 12, 2008 #1


    User Avatar
    Homework Helper
    Gold Member

    Ok, I'm given this polynomial and I'm asked to find the roots of it in the ring mod p.

    And then it asks to do it in, mod p^2, mod p^3 and mod p^4.

    I don't remember ever learning how to do it in those powers.

    Any tips on how to solve such things?

    Note: Without having to sub in all the values. If it was 7^4, that would suck.

    Note: Not homework. It's just a problem set to a pdf file I'm going through. It's review for the material, so I want to get a handful of problems down before moving forward.
  2. jcsd
  3. Oct 12, 2008 #2


    User Avatar
    Science Advisor
    Homework Helper

    Well if f(x)=0(mod p^k) then f(x)=0(mod p). Maybe this will help.
  4. Oct 13, 2008 #3


    User Avatar
    Homework Helper
    Gold Member

    Well, if you look at something mod 49, we can have f(43) = 0 mod 49, but I don't really care that f(43) = 0 mod p. I know that already.

    I would still have to check all the numbers up to 49 to see if there are any roots.
  5. Oct 13, 2008 #4


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    No you don't. You only have to check a few of them....
  6. Oct 15, 2008 #5
    if f(k)=0 (mod7)

    if you know roots of mod p
    and that is denoted as k_1, k_2, k_3, ...
    roots of mod p^2 will be
    p+k_1, 2p+k_1, 3p+k_1, ... , np+k_1,
    p+k_2, 2p+k_2, 3p+k_2, ... , np+k_2,
    p+k_3, 2p+k_3, 3p+k_3, ... , np+k_3,
    Last edited: Oct 15, 2008
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: Solving Polynimals in the ring mod p^r
  1. Polynomials (mod p) (Replies: 3)

  2. Integers mod p (Replies: 4)

  3. R/A mod out by A ? (Replies: 4)