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question on diophantine equations in Mathematica


Hi all,
I've installed trial of Mathematica 8.
I would like to search for possible solutions of diophantine equation
x^10+y^10+z^10=t^2.
How to do this efficiently?
FindInstance seems to be VERY slow! And indeed it doesn't always find every
solution of diophantine equations. For example I've tried it with
x^4+y^4+z^4=t^4 and it didn't find anything (but there are solutions!).
And Solve command just don't want to search! With some seconds it gives
During evaluation of In[1]:= Solve::svars: Equations may not give solutions
for all "solve" variables. >>
I will be very glad if someone make INDEED FAST algorithm for searching.

Ivan


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