Solving x^2+n*y^2=a without factoring positive $n$?

Georgi Guninski on Thu, 28 Nov 2019 16:52:09 +0100

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Solving x^2+n*y^2=a without factoring positive $n$?

To: pari-dev@pari.math.u-bordeaux.fr
Subject: Solving x^2+n*y^2=a without factoring positive $n$?
From: Georgi Guninski <gguninski@gmail.com>
Date: Thu, 28 Nov 2019 17:51:54 +0200

thue() appears to solve x^2+n*y^2=a without factoring
positive $n$ when we declare n as prime via addprimes():

? p=nextprime(2*10^8);q=nextprime(3*p);n=p*q;a=(p-1)^2+n*200^2;addprimes([n]);K=
thue(thueinit(x^2+n,0),a)

Given n and factored a, what is the complexity of solving the
equation? (the solution is bounded by sqrt(a))

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  - From: Bill Allombert <Bill.Allombert@math.u-bordeaux.fr>

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