Re: Any chance to compute system of Diophantine exquations in 26 variables in GP?

[Bill Allombert <Bill.Allombert@math.u-bordeaux.fr>]

On Mon, Jan 29, 2024 at 10:46:44AM +0100, hermann@stamm-wilbrandt.de wrote:
> On 2024-01-26 20:28, Bill Allombert wrote:
> > 
> > The issue is that the smallest solution is doubly exponential in k^4,
> > so you will probably not be able to compute it.
> > ...
> > but then
> > p=(n+1)^k
> > q=(p+1)^n
> > 
> > is going to be too large.

> Perhaps some kind of optimized backtracking algorithm (utilizing GP where
> helpful)
> will be able to determine variable settings for small k in reasonable amount
> of time?

The problem is that the value of q for example is so large it will not fit in
the memory of your computer...

Cheers,
Bill