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Old 2012-03-03, 22:24   #1
Stargate38
 
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Default 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?
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Old 2012-03-03, 23:16   #2
Batalov
 
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Quote:
Originally Posted by Stargate38 View Post
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)
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Old 2012-03-04, 00:59   #3
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Quote:
Originally Posted by Batalov View Post
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)))
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Old 2012-03-04, 20:03   #4
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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.
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Old 2012-03-04, 22:36   #5
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PARI has factor_Aurifeuille, but I don't think it's exposed to gp.
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Old 2012-03-05, 05:39   #6
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Here is a link to a paper where aurifeuillian factorization was implemented
in gp/pari. You could request to get the code.
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Old 2012-03-05, 06:05   #7
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Quote:
Originally Posted by jcrombie View Post
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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