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

"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^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 (wingler@math.ysu.edu)

Dept. of Mathematics and Statistics

Youngstown State University

One University Plaza

Youngstown, OH 44555-0001

330-941-1817