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Old 2006-06-05, 21:19   #3
R. Gerbicz
 
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"Robert Gerbicz"
Oct 2005
Hungary

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There was also an error in N:

N=2,1526L/2,218L=2^654+2^600+2^545-2^436-2^382-2^327-2^273-2^218+2^109+2^55+1

I think the correct polynom ( I've found this by hand ) is the following: (checking this by Pari-Gp ):

(23:15) gp > f(x)=x^6+2*x^5-10*x^4-20*x^3+16*x^2+32*x+8
(23:15) gp > g(z)=substpol(f(x),x,2*z+1/z)
%4 = (64*z^12 + 64*z^11 + 32*z^10 - 16*z^8 - 16*z^7 - 8*z^6 - 8*z^5 - 4*z^4 + 2*z^2 + 2*z + 1)/z^6
(23:15) gp >

Further checking to see that g(z) has a root of 2^54 modulo N:

(23:28) gp > lift(g(Mod(2^54,N)))
%13 = 0
(23:28) gp >

Last fiddled with by R. Gerbicz on 2006-06-05 at 21:30
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