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Georgi Guninski on Tue, 08 Dec 2020 15:41:28 +0100
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Re: Can bnfinit recognize square integer factors without factorization?
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- To: pari-dev@pari.math.u-bordeaux.fr
- Subject: Re: Can bnfinit recognize square integer factors without factorization?
- From: Georgi Guninski <gguninski@gmail.com>
- Date: Tue, 8 Dec 2020 16:41:14 +0200
- Delivery-date: Tue, 08 Dec 2020 15:41:28 +0100
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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