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Re: b^p = 1 mod q^3

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  • djbroadhurst
    ... Get Pari-GP to do it for you :-) Assuming that p|q-1, with prime q, we simply ask for bsol(p,q)=lift(znprimroot(q^3)^(q^2*(q-1)/p)); example:
    Message 1 of 2 , Oct 2, 2011
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      --- In primenumbers@yahoogroups.com,
      Kermit Rose <kermit@...> wrote:

      > Suppose b0^p = 1 mod q, where q is prime.
      > Let b = (b2 q^2 + b1 q + b0)
      ...
      > Use formula for (b2 q^2 + b1 q + b0)^p to find
      > expansion mod q^3.
      > If I were more familiar with that formula,
      > I could do it here.

      Get Pari-GP to do it for you :-)

      Assuming that p|q-1, with prime q,
      we simply ask for

      bsol(p,q)=lift(znprimroot(q^3)^(q^2*(q-1)/p));
      \\ example:
      b=bsol(5,11);if(Mod(b,11^3)^5==1,print(b));

      1170

      David
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