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exponential diophantine equations

• To: mathgroup at smc.vnet.net
• Subject: [mg62922] exponential diophantine equations
• From: Andrea <andrea at radargift.com>
• Date: Thu, 8 Dec 2005 03:27:32 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

I'm trying to find out how to use Mathematica to find solutions to 
exponential diophantine equations like the following:

         (5x)^2 - 2^k * 3 * (5+k)^2 - 131 * k + 7 = 0.   I want to obtain 
solutions for x and k. (One solution is x = 31, k = 6, but I didn't find 
this using Mathematica!)

I'm not very skilled in Mathematica. I tried Solve and Reduce but I just 
get either

The equations appear to involve the variables to be solved for in an 
essentially non-algebraic way.
or
This system cannot be solved with the methods available to Reduce.

I'm trying to find a way to get at least one or two solutions. Is there a 
way in Mathematica to do this? I know that exponential ones are not easy...

Thanks for any help.

Andrea  

• Follow-Ups:
  • Re: exponential diophantine equations
    • From: Andrzej Kozlowski <akoz@mimuw.edu.pl>