> 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