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Topic: Number theory question continued
Replies: 9   Last Post: Mar 27, 2006 5:13 PM

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Dr. Eric Wingler

Posts: 139
Registered: 12/12/04
Re: Number theory question continued
Posted: Mar 27, 2006 2:25 PM
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"ManOfLight" <mladensavov@yahoo.com> wrote in message
> 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

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