• Support PF! Buy your school textbooks, materials and every day products Here!

Find All Integers Such that phi(n)=12

  • Thread starter cwatki14
  • Start date
  • #1
57
0
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?
-Thanks
 

Answers and Replies

  • #2
236
0
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?
 
  • #3
57
0
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?
[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?
 

Related Threads for: Find All Integers Such that phi(n)=12

Replies
3
Views
1K
Replies
16
Views
3K
Replies
19
Views
5K
Replies
12
Views
953
  • Last Post
Replies
6
Views
4K
  • Last Post
Replies
8
Views
2K
Replies
5
Views
755
Top