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Re: Number theory question continued
Posted:
Mar 27, 2006 2:25 PM


"ManOfLight" <mladensavov@yahoo.com> wrote in message news: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^n3^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's possible that you may be able to make use of the density of the set of numbers of the form m*log(3)  n*log(2).
________________________________ Eric J. Wingler (wingler@math.ysu.edu) Dept. of Mathematics and Statistics Youngstown State University One University Plaza Youngstown, OH 445550001 3309411817



