Re: What’s the equivalent of Mathematica’s Solve[] Function in Pari/Gp ?

["Thomas D. Dean" <tomdean@wavecable.com>]

On 1/12/25 03:14, Bill Allombert wrote:
> On Sun, Jan 12, 2025 at 11:46:43AM +0100, Laël Cellier wrote:
> > No,
> >
> > it stops after finding the first solution instead of returning every
> > possible values and that’s what I’m needing.
>
> Given the size of the solution it cannot just try all integers until finding
> one that works, it must do something smarter.
>
> > And even if gcdext was the
> > solution, how would I be able to use it since the equation contains a ==
> > sign ?
>
> Every equation contains a equal sign by definition.
>
> Set
> RSA260=22112825529529666435281085255026230927612089502470015394413748319128822941402001986512729726569746599085900330031400051170742204560859276357953757185954298838958709229238491006703034124620545784566413664540684214361293017694020846391065875914794251435144458199
>
> F=(sqrtint(RSA260)+1)^2
>
> You want to solve
>
> ((25)^2 + x RSA260)/(y) == F
>
> after multiplying by y one get:
>
> x*RSA260 -F*y == -(25^2)
>
> Compute
> [X,Y,d]=gcdext(RSA260,F)
> we find d=1 so
> X*RSA260 + Y*F == 1
> So you just need to multiply by -(25^2)
> -(25^2)*X*RSA260 -(25^2)*Y*F == -(25^2)
> hence the solution is
>
> x = -(25^2)*X
> y = (25^2)*Y

Mathematica indicates there are an infinite number of solutions in the 
integers by including the constant C[1] in the solution. Maple uses _Z1.

Tom Dean