PRIME REPETENDS 1/Q
- Thanks so much for your responses and I've been still staring at
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
--- In firstname.lastname@example.org, Alan Eliasen <eliasen@m...>
> patience_and_fortitude wrote:factors of
> > 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
> anything but 2 and/or 5, it will *always* produce a repeatingdecimal.
> If the denominator has only factors of 2 and 5, or, more
> 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
> denominator. That is, if the denominator is, say, 17, the decimalwill
> repeat after 17 digits or less. You can see why this happens byworking
> some samples out with long division.Deming
> 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