--- 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