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Old 2005-08-18, 14:49   #3
alpertron's Avatar
Aug 2002
Buenos Aires, Argentina

2·11·61 Posts

Unfortunately with the following code:

10   input N0
20   N=2^(2^N0)+1
30   Ii=modpow(2,2^(N0-1),N)
40   Ii2=modpow(2,2^(N0-2),N)
50   Ii3=modpow(2,2^(N0-3),N)
60   Sq2=(Ii2*2*modinv((1+Ii),N))@N
70   Sq2a=(Ii3*2*modinv((Ii*Sq2+1-Ii),N)@N)
80   print Sq2,Sq2^2@N
90   print ((Sq2a*Sq2a)-2)@N
I found that the values of sqrt(2) generated by calculating directly the sqrt(2) and calculating B=sqrt(2+sqrt(2)) and then B^2-2 = sqrt(2) are the same, so they cannot be used to factor Fn.
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