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Bill Allombert on Wed, 10 Jul 2024 12:44:39 +0200
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Re: Question: trying to locate other Diophantine triples from certain elliptic curves
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- To: pari-users@pari.math.u-bordeaux.fr
- Subject: Re: Question: trying to locate other Diophantine triples from certain elliptic curves
- From: Bill Allombert <Bill.Allombert@math.u-bordeaux.fr>
- Date: Wed, 10 Jul 2024 12:44:33 +0200
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On Wed, Jul 10, 2024 at 05:26:39AM -0500, Kurt Foster wrote:
> On Jul 8, 2024, at 6:25 PM, American Citizen wrote:
>
> > To all:
> >
> > I want to keep pursuing this question
> >
> > We have an associated Elliptic Curve associated with a Diophantine
> > Triple [a,b,c] where a*b+1, a*c+1 and b*c+1 are all squares.
> >
>
> The following paper (and its references) may be of interest:
>
> Dujella, Andrej
> Diophantine m-tuples and elliptic curves
> Journal de Théorie des Nombres de Bordeaux, tome 13, no 1 (2001), p. 111 -
> 124
Also Andrej just published a whole book on this topic:
Diophantine m-tuples and Elliptic Curves
https://link.springer.com/book/10.1007/978-3-031-56724-7
which contains GP examples code.
Cheers,
Bill