PRIME REPETENDS 1/Q

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• Thanks so much for your responses and I ve been still staring at these things. So the summary is: [P, Q, are primes other than 3; R is the repeating part of
Message 1 of 6 , Jul 29, 2005
Thanks so much for your responses and I've been still staring at
these things.

So the summary is:

[P, Q, are primes other than 3; R is the repeating part of the
repetend, n is the number of repeating digits]

statement 1: P/Q always yields some R
statement 2: n <= Q
statement 3: R mod 9 = 0

and I might add a couple more trivial ones:

R is always odd (I.E not 18, 36 etc..)
Also R mod P = 0

so really R mod 9P = 0

It seems that the numerator prime P is irrelevant to this discussion
acnd could be factored out for simplicity,
1/Q yields a repetend "r" where r mod 9 = 0.

So this means each prime has a corrosponding r/9 number.
Question: Is it necessarily unique?; I would think so, but I've never
been too good at thinking through all the logical consequences of
that.

-Shawnbob

--- In primenumbers@yahoogroups.com, Alan Eliasen <eliasen@m...>
wrote:
> patience_and_fortitude wrote:
> > If you divide one prime by another, it generally results in a
> > repeating decimal of some length.
>
> It might be helpful to clarify that if the denominator has
factors of
> anything but 2 and/or 5, it will *always* produce a repeating
decimal.
>
> If the denominator has only factors of 2 and 5, or, more
specifically
> 2^n and 5^m, the decimal part will terminate after at most max(n,m)
digits.
>
> The maximum length of the part that repeats can be no bigger
than the
> denominator. That is, if the denominator is, say, 17, the decimal
will
> repeat after 17 digits or less. You can see why this happens by
working
> some samples out with long division.
>
> --
> Alan Eliasen | "It is not enough to do your best;
> eliasen@m... | you must know what to do and THEN
> http://futureboy.homeip.net/ | do your best." -- W. Edwards
Deming
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