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Bill Allombert on Wed, 10 Jul 2024 16:58:43 +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 16:58:39 +0200
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On Tue, Jul 09, 2024 at 07:46:39PM -0700, American Citizen wrote:
> I appreciate all your effort, Bill and John
>
> Somehow, someway, something got sideways.
>
> The Diophantine condition is that (a*b+1), (a*c+1) and (b*c+1) are squares.
> I don't understand how this got changed to (a*b), (a*c) and (b*c) squares.
>
> Can we start over again, with this understanding?
We understood your question as:
Given a,b,c, find A,B,C so that
E_triple(a,b,c) and E_triple(A,B,C) are isomorphic.
I think we addressed that.
Cheers,
Bill.