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Question: Finding the Blue Bird of Happiness with Maple

Question:Finding the Blue Bird of Happiness with Maple

Markiyan Hirnyk 7759 Maple
diophantine_equation
April 01 2012
0

How to solve the equation 2017*x^2013+2015*y^2013-2033*z^2013-2011 = 0 over the integers with Maple?
I tried it with the Direct Search v.2 package:
>with(DirectSearch):
>SolveEquations([2017*x^2013+2015*y^2013-2033*z^2013-2011 = 0], {z > -100000, x >= -100000, y >=-10000, x<= 10000, y <= 10000, z <= 10000, assume=integer, AllSolutions);
In view of it possible solutions are very big. I suppose the equation under consideration  has no integer solutions. John May is my hope to solve that.
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