Bill Allombert on Sat, 26 Dec 2009 15:48:43 +0100

 Re: Montgomery Square Root question

```On Sat, Dec 26, 2009 at 03:25:08PM +0100, Bill Allombert wrote:
> Let P=a^3+60*a+64 and z your number expressed in term of a, not x:
> P=a^3+60*a+64
> z=2814657884122787163746793632808511761633499567234431374441483926978867652153721301870381570719744*a^2-40942132939331751018273240650591985707497862567514861324721751201493425821910113619606396083372032*a-45975747055689337511796545375440934437650258546148057739453165564673458691658141449930516266483712
>
> then do
> nfroots(P,x^2-z)

Actually with PARI 2.3 you should do (this should be faster anyway):
K=nfinit(P);
nfroots(K,x^2-z)
%4 = [Mod(-189133117686159822165485681043654738588680060928*a^2 - 2055476375095129701009302875309311162506447683584*a - 1945600371033366152866700970896778949964215615488, a^3 + 60*a + 64), Mod(189133117686159822165485681043654738588680060928*a^2 + 2055476375095129701009302875309311162506447683584*a + 1945600371033366152866700970896778949964215615488, a^3 + 60*a + 64)]

Cheers,
Bill.

```