Re: How to find a solution to this equation so the result is a postive perfect square ?

[Denis Simon <denis.simon@unicaen.fr>]

A possibility to get positive solutions is to choose Y first, randomly, smaller than the square root of N.
Then
Z = lift(Mod(Y/s,a))
X = -(Y^2-N*Z^2)/a;
This will only work if s is coprime to a, or equivalently if N is coprime to a.

Denis SIMON.

----- Mail original -----
> De: "Laël Cellier" <lael.cellier@laposte.net>
> À: "pari-users" <pari-users@pari.math.u-bordeaux.fr>, "Denis Simon" <denis.simon@unicaen.fr>
> Envoyé: Jeudi 13 Février 2025 20:28:56
> Objet: Re: How to find a solution to this equation so the result is a postive perfect square ?

> Bon soir,
> 
> sorry. I recognize this wasn’t clear beside the square of a negative
> integer is always positive (-Y²=Y² always). But I want positive integers
> as solution to the equation… It seems your proposal will always lead to
> negative perfect squares whereas the first example show positive
> solutions can exists…
> 
> Cordialement,