Re: Is it possible to have several solutions in this way to this equation using Pari/ɢᴘ ?

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

On Sun, Jan 19, 2025 at 11:58:47AM +0100, Laël Cellier wrote:
> Bonjour,
> 
> I’ve the following equation where the aim is to find /alpha/ and /beta/ as
> integers given /w/ and /v/ as integers
> 
> alpha == w (v + w beta)

> Of course finding several solution for the equation above is possible, but
> then I want /nfroots()/ to return a second set of possible results given /c/
> and /b/ and where /x/ is an unknow
> 
> xx=alpha^2*x^2+(2*alpha*beta-abs(b))*x+(beta^2-c);
> nfroots(,xx);

So given v,w,b,c you want to find integers alpha, beta and rational x such that

alpha = w *(v + w * beta)
alpha^2*x^2+(2*alpha*beta-abs(b))*x+(beta^2-c) = 0

Is it correct ? 

Cheers,
Bill.