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PRIME REPETENDS 1/Q

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  • patience_and_fortitude
    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
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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 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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