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