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question on diophantine equations in Mathematica

• To: mathgroup at smc.vnet.net
• Subject: [mg115479] question on diophantine equations in Mathematica
• From: Ivan Smirnov <ivan.e.smirnov at gmail.com>
• Date: Tue, 11 Jan 2011 19:25:26 -0500 (EST)

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