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!

Generator (number theory)

  1. Oct 30, 2007 #1
    1. The problem statement, all variables and given/known data

    Let a be a generator of [tex]F_q[/tex]

    Prove that [tex]a^i[/tex] is a generator if & only if [tex]i[/tex] and [tex]q-1[/tex] are relatively prime.


    2. Relevant equations

    a is a generator of [tex]F_q[/tex] means that a^(q-1) = 1 and [tex]a^i[/tex] cannot be 1 for all i not q-1.

    relatively prime means that [tex]gcd(i,q-1)[/tex]=1

    fermats theorem says that: a^(p-1) = 1 (mod p ) where p is prime

    3. The attempt at a solution

    =>
    Suppose that [tex]a^i[/tex] is a generator of [tex]F_q[/tex]. then a^(i(q-1)) =1 (mod q)

    so by fermats theorem, gcd(i, q-1) = 1???

    How does that sound?
     
  2. jcsd
  3. Oct 31, 2007 #2
    Think of the subgroup generated by a^i.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Generator (number theory)
  1. Number Theory (Replies: 2)

  2. Number theory ! (Replies: 4)

  3. Number Theory (Replies: 2)

  4. Number Theory (Replies: 11)

  5. Number theory (Replies: 5)

Loading...