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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?
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