mersenneforum.org Aurifeuillian Factors of n^x±1?
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 2012-03-03, 22:24 #1 Stargate38     "Daniel Jackson" May 2011 14285714285714285714 11338 Posts Aurifeuillian Factors of n^x±1? Can someone please give me some Pari/gp input code for the Aurifeuillian factors of nx±1 for arbitrary n?
2012-03-03, 23:16   #2
Batalov

"Serge"
Mar 2008
Phi(4,2^7658614+1)/2

912310 Posts

Quote:
 Originally Posted by Stargate38 Can someone please give me some Pari/gp input code for the Aurifeuillian factors of nx±1 for arbitrary n?
Use these examples:
Code:
factor(5^5*N^10-1)
factor(7^7*N^14+1)

2012-03-04, 00:59   #3
science_man_88

"Forget I exist"
Jul 2009
Dumbassville

8,369 Posts

Quote:
 Originally Posted by Batalov Use these examples: Code: factor(5^5*N^10-1) factor(7^7*N^14+1)
thanks you gave me a way to get to :

Code:
forprime(X=1,1000,a=factor(N^X-1);N=2;print(a=eval(a)))

 2012-03-04, 20:03 #4 jcrombie     "Jonathan" Jul 2010 In a tangled web... 2×107 Posts Hi Stargate38, I've just posted a link over in this thread for a .cpp program. It's not in pari (but makes pari calls), so not exactly what you were asking for. Feel free to steal whatever you like! Last fiddled with by jcrombie on 2012-03-04 at 20:05 Reason: link didn't work.
 2012-03-04, 22:36 #5 CRGreathouse     Aug 2006 10111001001102 Posts PARI has factor_Aurifeuille, but I don't think it's exposed to gp.
 2012-03-05, 05:39 #6 jcrombie     "Jonathan" Jul 2010 In a tangled web... 110101102 Posts Here is a link to a paper where aurifeuillian factorization was implemented in gp/pari. You could request to get the code.
2012-03-05, 06:05   #7
CRGreathouse

Aug 2006

2×2,963 Posts

Quote:
 Originally Posted by jcrombie Here is a link to a paper where aurifeuillian factorization was implemented in gp/pari. You could request to get the code.
That's the factor_Aurifeuille I mentioned above. It's a part of PARI but not exposed to gp. You can use load it into gp with the command they give in the paper
Code:
install(factor_Aurifeuille, GL);
but I suspect this will not work for people using the Windows version unless they compiled it on their own. It works fine on Linux.

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