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

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Jens Kruse Andersen

Posts: 53
Registered: 12/13/04
Re: Number theory question continued
Posted: Mar 25, 2006 11:52 AM
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ManOfLight wrote:

> "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?"

I find this formulation a little unclear. I guess it means:
"Is it true that for sufficiently large L, every interval of length L will
contain an integer of the form 2^n-3^m?"

This is trivially equivalent to:
Does there exist H such that for every y, the interval [y, y+H] contains an
integer on the form 2^n-3^m?

> 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.

That matches my interpretation.

If the answer is no then you must prove:
For every H, there exists y such that the interval [y, y+H] does not contain
an integer on the form 2^n-3^m.

Jens Kruse Andersen

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