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

Homework Help: Primitive roots, specifically of 18

  1. Mar 11, 2005 #1
    this problem is annoying. ive found that the primitive roots of 9 are 2 and 5. since 2|18 it cant be a root. i know via some theorems in my book that if 5 is a primitive root of 3, then its a primitive root of 3^k, and also of 2*3^k.

    sorry about not using latex, shouldnt need it for this one though, it wont be too messy im sure.

    so the second one, i know i can find by brute force, but id like something more elegant. i know there are only phi of phi of 18, or 2, primitive roots.

    i know also by table lookup that the second one of 18 is 11.

    do i need to start with the gcd(a,18) list and just eliminate ones until i cant eliminate 11? that doesnt seem right, i remember seeing something in class about this, but the teacher said not to record it in notes because it was in the book, but the book only identifies the one, because i think it is always the smallest. or do i just take 2 mod 9 congruent to 11 mod 9, and thats it? sorry if i just missed something plain as day.
     
  2. jcsd
  3. Mar 11, 2005 #2

    Hurkyl

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Bleh, it took a minute to figure out about what you're talking.

    Did you notice that 11 is a primitive root of 9? (and of 3)
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook