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

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Phil Carmody

Posts: 2,219
Registered: 12/7/04
Re: Number theory question continued
Posted: Mar 25, 2006 6:45 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

"ManOfLight" <mladensavov@yahoo.com> writes:

> 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.


Trivially true by invoking the principle of vacuousity.

Proof:
Any interval not containing such a value is insufficiently large.

Phil
--
What is it: is man only a blunder of God, or God only a blunder of man?
-- Friedrich Nietzsche (1844-1900), The Twilight of the Gods



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