1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Pocklington's Criterion?

  1. Aug 9, 2006 #1

    CRGreathouse

    User Avatar
    Science Advisor
    Homework Helper

    http://mathworld.wolfram.com/PocklingtonsCriterion.html

    I'm confused by the statement of this theorem. Either there's a mistake in the explanation, or I'm missing something pretty big.

    Let me take an example and go through step by step. Let p=3 and k=4. p is an odd prime and 1 <= 4 <= 8. 3 does not divide 4.

    The statement on MathWorld seems to say that 1 and 2 are equivilent:
    1. 25 = 2 * 4 * 3 + 1 is prime.
    2. There exists an a such that GCD(a^4+1, 25)=1.

    5*5=25 is not prime. Checking briefly:
    GCD(1,25)=1
    GCD(2,25)=1
    GCD(17,25)=1
    GCD(82,25)=1
    GCD(257,25)=1
    GCD(626,25)=1

    What am I misunderstanding?
     
  2. jcsd
  3. Aug 10, 2006 #2

    shmoe

    User Avatar
    Science Advisor
    Homework Helper

    Odd, Mathworld seems to leave out a couple of conditions. You also need

    2<=a<N

    and

    N divides a^(kp)+1

    for condition 2.

    This is in Ribenboim's My Numbers, My Friends.
     
  4. Aug 10, 2006 #3

    CRGreathouse

    User Avatar
    Science Advisor
    Homework Helper

    I knew there was something. The entry was overly sparse.

    Thanks!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Pocklington's Criterion?
Loading...