1. Limited time only! Sign up for a free 30min personal 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!

Homework Help: Find All Integers Such that phi(n)=12

  1. Mar 11, 2010 #1
    I am trying to find all of the integers such that phi(n)=12. Clearly n=13 is one, but how do I do it for composite numbers?
  2. jcsd
  3. Mar 11, 2010 #2
    What can you say about [tex]\varphi(a)\varphi(b)[/tex] with regard to [tex]\varphi(ab)[/tex]? What about [tex]\varphi(p^n)[/tex] if p is prime?
  4. Mar 11, 2010 #3
    [tex]\varphi(a)\varphi(b)[/tex]=[tex]\varphi(ab)[/tex] if (a,b)=1. [tex]\varphi(p^n)[/tex]= [tex]\(p^n)[/tex]-[tex]\(p^n-1)[/tex] if p is prime. So am I looking for all combinations of n in which the respective phi(n) add to equal 12? I.E. am I searching for prime factorizations of some n where these two properties will yield of phi of 12?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook