```Date: Mar 27, 2006 2:25 PM
Author: Dr. Eric Wingler
Subject: Re: Number theory question continued

"ManOfLight" <mladensavov@yahoo.com> wrote in messagenews:1143276915.440583.51260@z34g2000cwc.googlegroups.com...> Hello everybody,>   I post it again to rapair one mistake>   Could you give a clue how I can start the following problem or> propose a solution.>>> "Is it true that for every sufficiently large interval there will be a> integer in it of the form>   2^n-3^m where m,n are integers?">>>  As far as I understand it we are supposed either to prove that there> exists number H : every interval with length H contains such a number> or disprove it.If  x = 2^n - 3^m,  then  log(1 - x/2^n) = m*log(3) - n*log(2), so it'spossible that you may be able to make use of the density of the set ofnumbers of the form   m*log(3) - n*log(2).________________________________Eric J. Wingler  (wingler@math.ysu.edu)Dept. of Mathematics and StatisticsYoungstown State UniversityOne University PlazaYoungstown, OH  44555-0001330-941-1817
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