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

[Laël Cellier <lael.cellier@laposte.net>]

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 I need to find several possible valid values of alpha and beta such as a different set of roots from xx are found in the last step based on different alpha and beta. Is it something possible ? If yes, how to do it 

currently, I’m using this code to find alpha and beta :

beta=-(V\W);

alpha=W*(V+W*beta);

print("alpha=",alpha);

print("beta=",beta);

where W is a perfect square and V an integer.

Cordialement,