Re: Question: trying to locate other Diophantine triples from certain elliptic curves

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

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