I translated the sqrt(2) program to UBASIC

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 Sq2=(Ii2*2*modinv((1+Ii),N))@N
60 print Sq2,Sq2^2@N

This is interesting, but it would be far more interesting to find another sqrt(2) that is not the negative of this one (mod F

_{n}). This would allow to factor F

_{n} and you will appear in math books :-) .