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MathGroup Archive 2005

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Re: exponential diophantine equations

  • To: mathgroup at smc.vnet.net
  • Subject: [mg62931] Re: [mg62922] exponential diophantine equations
  • From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
  • Date: Thu, 8 Dec 2005 06:25:35 -0500 (EST)
  • References: <200512080827.DAA17940@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

On 8 Dec 2005, at 17:27, Andrea wrote:

>
> 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!)

Are you sure you have found a solution? I get:

In[30]:=
(5x)^2 - 2^k * 3 * (5+k)^2 - 131 * k + 7 /.{x->31,k->6}

Out[30]=
14


One can certianly try some "educated searches" but before starting it  
woudl be better to be sure that this is really the equation you want  
to solve!

Andrzej Kozlowski


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