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

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

Hi,

and what would be the code to solve
a×x + sqrt(b×y²) = c in {x,y} integers

instead ? The aim is to have b×y being a perfect square and if possible have a value lower than a…
Cordialement,

Le 12/01/2025 à 11:58, Karim Belabas a écrit :
> Hi Laël,
>
>    Bill's question was about the algorithm used, not the result.
>
> To solve a*x + b*y = c in {x,y} integers (given a,b,c integers) in GP:
>
> Solve(a,b,c) =
> { my([u, v, d] = gcdext(a, b));
>
>    if (c % d, return ([]));  \\ no solution
>    my(x = c/d * u % (b/d));
>    [x, (c - a*x) / b];
> }
>
> ? Solve(300001,4139891237,5)
> %1 = [1952821586, -141513]
> ? 1952821586 * 300001 - 141513*4139891237
> %2 = 5
>
> Cheers,
>
>      K.B.