Re: Can bnfinit recognize square integer factors without factorization?

[Georgi Guninski <gguninski@gmail.com>]

On Sun, Dec 6, 2020 at 7:29 PM Bill Allombert
<Bill.Allombert@math.u-bordeaux.fr> wrote:

> > n=p^2*q;addprimes(n);K=bnfinit(x^2+n);
> >

> ? quadclassunit(-n)
> %12 = [603602686944,[603602686944],[Qfb(679298724049,-45901789467,1692713557093)],1]
>
> n is not prime since the class number is even.
> Not sure how one can conclude that n is not squarefree.
>

Thanks. I believe if you can find the class number, you can factor
the integer n.

A Rigorous Time Bound for Factoring Integers

https://www.researchgate.net/publication/28639458_A_Rigorous_Time_Bound_for_Factoring_Integers