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

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

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

Cheers,
Bill.