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What inspite FindInstance

• To: mathgroup at smc.vnet.net
• Subject: [mg122731] What inspite FindInstance
• From: Artur <grafix at csl.pl>
• Date: Tue, 8 Nov 2011 07:15:12 -0500 (EST)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• Reply-to: grafix at csl.pl

Dear Mathematica Gurus,
Matematical problem is following: find pair of integres {d,x} which fill 
equation (d ^2 +
      270 d Root[1 - 270 #1^3 - 5832 #1^5 + 3645 #1^6 &, 1]^3 -
      2916 x Root[1 - 270 #1^3 - 5832 #1^5 + 3645 #1^6 &, 1]^5 +
      3645 Root[1 - 270 #1^3 - 5832 #1^5 + 3645 #1^6 &, 1]^6 ==
     0)

FindInstance[(d ^2 +
      270 d Root[1 - 270 #1^3 - 5832 #1^5 + 3645 #1^6 &, 1]^3 -
      2916 x Root[1 - 270 #1^3 - 5832 #1^5 + 3645 #1^6 &, 1]^5 +
      3645 Root[1 - 270 #1^3 - 5832 #1^5 + 3645 #1^6 &, 1]^6 ==
     0) && (x d != 0), {x, d}, Integers]

Mathematica report:
FindInstance::nsmet: The methods available to FindInstance are 
insufficient to find the requested instances or prove they do not exist. >>

First solution is x=2 and d=-1
I'm looking for next ones. Who have idea what to do?

Best wishes
Artur

• Follow-Ups:
  • Re: What inspite FindInstance
    • From: Daniel Lichtblau <danl@wolfram.com>
  • Re: What inspite FindInstance
    • From: Andrzej Kozlowski <akoz@mimuw.edu.pl>