Re: question on diophantine equations in Mathematica

*To*: mathgroup at smc.vnet.net*Subject*: [mg115496] Re: question on diophantine equations in Mathematica*From*: Andrzej Kozlowski <akoz at mimuw.edu.pl>*Date*: Thu, 13 Jan 2011 03:23:31 -0500 (EST)

This seems to show that there are only trivial solutions for 1<=t<=90000 Timing[ Select[Table[ PowersRepresentations[t^2, 3, 10], {t, 1, 90000}], #1 != {} & ]] {0.8722430000000259, {{{0, 0, 1}}, {{0, 0, 2}}, {{0, 0, 3}}, {{0, 0, 4}}, {{0, 0, 5}}, {{0, 0, 6}}, {{0, 0, 7}}, {{0, 0, 8}}, {{0, 0, 9}}}} The algorithm basically uses "brute force" so you will start getting overflows for very large t. Andrzej Kozlowski On 12 Jan 2011, at 01:25, Ivan Smirnov wrote: > 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