"ManOfLight" <email@example.com> wrote in message news:firstname.lastname@example.org... > 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'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 (email@example.com) Dept. of Mathematics and Statistics Youngstown State University One University Plaza Youngstown, OH 44555-0001 330-941-1817