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Any Relationship?

  1. Jul 2, 2004 #1
    Doing maths cousework, Phi Function and i came out with these numbers (i dnt no if it has anything do to with phi number yet)

    i) Φ (4²) = Φ(16) = 2
    ii) Φ (6²) = Φ(36) = 12
    iii) Φ (8²) = Φ(64) = 32

    its looks as if there could b a relatonship between them but i cant see one, can you?
    thanks

    Lokolo
     
  2. jcsd
  3. Jul 2, 2004 #2
    phi(16) != 2, since 1, 3, 5, 7, 9, 11, 13 and 15 are all coprime to 16. phi(16) = 8.
     
  4. Jul 2, 2004 #3
    opps yeh sorry, so do you think there will be a general forumla? i have got one for prime squares
    Φ(p²) = p² - p
    where p = prime
    but not one for all others
     
  5. Jul 2, 2004 #4
    Well... phi(ab) = phi(a)phi(b) if a and b are relatively prime, and phi(p^n) = p^n - p^(n - 1) where p is a prime and n a natural number. Those are the ones I know of. And of course, those two formulas taken together provide an easy way to compute phi(x) if you know the prime factorization of x.
     
    Last edited: Jul 2, 2004
  6. Jul 2, 2004 #5
    wow, i have a lot of testin to do....
    thanks muzza
     
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