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Bill Allombert on Mon, 29 Jan 2024 11:55:30 +0100
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Re: Any chance to compute system of Diophantine exquations in 26 variables in GP?
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- To: pari-users@pari.math.u-bordeaux.fr
- Subject: Re: Any chance to compute system of Diophantine exquations in 26 variables in GP?
- From: Bill Allombert <Bill.Allombert@math.u-bordeaux.fr>
- Date: Mon, 29 Jan 2024 11:54:58 +0100
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- In-reply-to: <3600bac8e37ef5817e2b8661901c2d4c@stamm-wilbrandt.de>
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- References: <9f454ef82d96ebd7401532329ff7bef9@stamm-wilbrandt.de> <ZbOI46rQIx62D8xd@seventeen> <ZbQH7hpx9dDOZIWC@seventeen> <3600bac8e37ef5817e2b8661901c2d4c@stamm-wilbrandt.de>
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