Results 1 to 2 of 2

Math Help - Period of fraction - Number Theory

  1. #1
    Newbie
    Joined
    May 2009
    Posts
    2

    Period of fraction - Number Theory

    Suppose (p,q) = 1, (p,10)=1 and (q,10)=1. if 1/p has period r and 1/q has period s find the period of 1/pq.

    Can anyone help - I've got the start but seem to have become stuck. Any help is much appreciated.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Opalg's Avatar
    Joined
    Aug 2007
    From
    Leeds, UK
    Posts
    4,041
    Thanks
    7
    Quote Originally Posted by jp3105 View Post
    Suppose (p,q) = 1, (p,10)=1 and (q,10)=1. if 1/p has period r and 1/q has period s find the period of 1/pq.

    Can anyone help - I've got the start but seem to have become stuck. Any help is much appreciated.
    If r is the period of 1/p then r is the smallest integer such that p divides 10^r-1. (Examples: 1/11 = 0.\overline{09} has period 2, and 11 divides 99 = 10^2-1; 1/37 = 0.\overline{027}, and 37 divides 999=10^3-1.)

    If 1/p has period r and 1/q has period s, and (p,q) = 1, then the smallest number of the form 10^t-1 that is a multiple of pq ought to be given by t=\text{lcm}(r,s).

    So the answer should be that the period of 1/(pq) is lcm(r,s). I'll leave you to fill in the details of that argument.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Textbooks on Galois Theory and Algebraic Number Theory
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: July 8th 2011, 06:09 PM
  2. Replies: 3
    Last Post: November 7th 2010, 06:10 PM
  3. Replies: 2
    Last Post: May 22nd 2010, 06:06 AM
  4. Chaos Theory: period points
    Posted in the Advanced Math Topics Forum
    Replies: 2
    Last Post: February 21st 2010, 09:13 AM
  5. Replies: 2
    Last Post: December 18th 2008, 05:28 PM

Search Tags


/mathhelpforum @mathhelpforum