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how to solve the integer equation Abs[3^x-2^y]=1

• To: mathgroup at smc.vnet.net
• Subject: [mg102988] how to solve the integer equation Abs[3^x-2^y]=1
• From: a boy <a.dozy.boy at gmail.com>
• Date: Thu, 3 Sep 2009 07:10:49 -0400 (EDT)

Does the equation |3^x-2^y|=1 give only 4 groups of solution?
(x,y)= (0,1),
          (1,1),
         (1,2),
          (2,3)

can anyone give any else solution?
when the two integers x and y become bigger and bigger, is there a
pair integer (x,y) to give a small value for  |3^x-2^y|? Or else,how
to prove the equation |3^x-2^y|=1having only 4 groups of integer
solution?

• Follow-Ups:
  • Re: how to solve the integer equation Abs[3^x-2^y]=1
    • From: Daniel Lichtblau <danl@wolfram.com>
  • Re: how to solve the integer equation Abs[3^x-2^y]=1
    • From: Andrzej Kozlowski <akoz@mimuw.edu.pl>