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
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