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>