Re: Can bnfinit recognize square integer factors without factorization?
Georgi Guninski <[email protected]>
| Newsgroups | gmane.comp.mathematics.pari.devel |
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| Message-ID | <CAGUWgD_XnQA32AxeUt+8gTB1-rUJ5WcZHrwmnuqczYDX4eYSig@mail.gmail.com> |
On Sun, Dec 6, 2020 at 7:29 PM Bill Allombert <[email protected]> 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