Re: How to solve the type of this simple diophantine equation with large Integers

Bill Allombert <[email protected]>
Newsgroups gmane.comp.mathematics.pari.user
Message-ID <Z81Ret3eJC-PFAo6@seventeen>
On Sun, Mar 09, 2025 at 01:22:17AM +0100, Laël Cellier wrote:
> Bonjour,simple question. I ve B and a semiprime A which are very large
> unrelated fixed integers impossible to factor.How to find y and z such as
> y²≡z²×B mod A? Which pari functions to use? Nfroots? Cordialement,

You best bet is zncoppersmith, but this will only work if there is a solution
(y,z) with relatively small y and z which will almost never be the case.

You need fundamentaly new ideas.

Cheers,
Bill.
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