       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:= 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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