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

[Kurt Foster <drsardonicus@earthlink.net>]

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

PDF at

http://www.numdam.org/item/JTNB_2001__13_1_111_0.pdf