Re: Big number division bug?

[James Wanless <james@grok.ltd.uk>]

Aha!
Thanks very much to both Karim and Robert...
I was (previously) unaware I was repeating factors (stupidly :) -  
should have tested them for primailty... and so was expecting the last  
result to be zero too.
Thanks again very much for your prompt and informative replies
J

On 28 Apr 2010, at 11:57, Karim Belabas wrote:

> * James Wanless [2010-04-28 12:41]:
> > I don't know if PARI is intended to handle such big numbers, but:
> >
> > ? (2^43112609+1)%(3*86225219*5259738299*5949540043)
> > %1 = 0
> > ? (2^43112609+1)%12482997260297
> > %2 = 0
> > ? (2^43112609+1)%453522086713962481
> > %3 = 0
> > ?  
> > (2 
> > ^ 
> > 43112609 
> > + 
> > 1 
> > ) 
> > %(3*86225219*5259738299*5949540043*12482997260297*453522086713962481)
> > %4 = 20781231343178972948687277924200040219405288340527425880342
> >
> > [GMP-ECM shows the same problem, so I don't know if it could even be
> > a bug in GMP???]
>
> I do not see a problem there : your moduli are not coprime
> ( in fact, 453522086713962481 divides  
> 3*86225219*5259738299*5949540043)
> so you can't deduce that the result should be 0 by the CRT.
>
> What result were you expecting ?
>
> Cheers,
>
>    K.B.
>
> P.S: The result given is consistent with the output of
>   N =  
> 3*86225219*5259738299*5949540043*12482997260297*453522086713962481
>   lift( Mod(2,N)^43112609 + 1 )
> which handles only tiny integers.
>
> --
> Karim Belabas, IMB (UMR 5251)  Tel: (+33) (0)5 40 00 26 17
> Universite Bordeaux 1          Fax: (+33) (0)5 40 00 69 50
> 351, cours de la Liberation    http://www.math.u-bordeaux.fr/~belabas/
> F-33405 Talence (France)       http://pari.math.u-bordeaux.fr/   
> [PARI/GP]
> `