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2012-04-02, 05:20   #1
princeps

Nov 2011

22·3 Posts
Proof of Primality Test for Fermat Numbers

Let $F_n$ be a Fermat number of the form :

$F_n=2^{2^n}+1$

Next , let's define sequence $S_i$ as :

$S_i=S^4_{i-1}-4\cdot S^2_{i-1}+2 ~ \text { with } ~ S_0=8$

Then :

$F_n ~; (n \geq 2) ~\text{ is a prime iff }~ F_n ~ \mid ~ S_{2^{n-1}-1$

Proof is attached . Any constructive comment is appreciated .
Attached Files
 FermatProof.pdf (169.1 KB, 125 views)