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• ... 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
--- 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

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