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April 24th, 2012, 04:27 PM  #1 
Math Team Joined: Dec 2006 From: Lexington, MA Posts: 3,267 Thanks: 408  An interesting fraction The decimal representation contains all the 3digit numbers except 998 [color=beige]. . [/color]and the 2997digit cycle repeats forever. This is just one of a family of such fractions. Can you determine the underlying characteristic? 
April 24th, 2012, 06:17 PM  #2 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs  Re: An interesting fraction
I looked at the factorization of the denominator, and found: So, next I looked at: Thus, I conjecture that the family you speak of is: where where the decimal representation contains all of the n digit numbers except and the period is . 

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