Loading ...
Sorry, an error occurred while loading the content.

Re: [PrimeNumbers] Q

Expand Messages
  • Phil Carmody
    ... Not just a circle, a wheel . ... They are the totatives . The number of them is the totient function, phi(). You can only list the totatives of N or
    Message 1 of 2 , Mar 30, 2007
    View Source
    • 0 Attachment
      --- Wes <6bullocks@...> wrote:
      > take the first three primes.
      >
      > multiply them together - 2*3*5 = 30
      >
      > Excluding these primes, and including the number 1 there is a symetry
      > that appears if a circle is drawn with circumference 30 units

      Not just a circle, a 'wheel'.

      > As is probably well known, each combination of possible residues is
      > represented for a total of (2-1)*(3-1)*(5-1) or 8. It is also
      > probably obvious that these 8 combinations of residues repeat for
      > each "30 circle" thereafter.
      >
      > So, here is the question: "What are the 8 numbers between 1 and 30
      > that are indivisible by 2, 3 and 5?" is there a known way to list
      > them? I was trying to say in my earlier posting that I do have a way
      > and that is what I'll describe next.

      They are the 'totatives'. The number of them is the totient function, phi().

      You can only list the totatives of N or evaluate phi(N) if you know the
      factorisation of N, or are prepared to work out the factorisation of N whilst
      so doing.

      That's given you a few terms to google. I'd guess Eric Weisstein's Mathworld is
      probably the best resource for this and related concepts.

      Phil

      () ASCII ribbon campaign () Hopeless ribbon campaign
      /\ against HTML mail /\ against gratuitous bloodshed

      [stolen with permission from Daniel B. Cristofani]



      ____________________________________________________________________________________
      Expecting? Get great news right away with email Auto-Check.
      Try the Yahoo! Mail Beta.
      http://advision.webevents.yahoo.com/mailbeta/newmail_tools.html
    Your message has been successfully submitted and would be delivered to recipients shortly.