20040910, 21:10  #1 
Feb 2004
France
2^{4}×59 Posts 
Two Primality tests for Fermat numbers
Hi,
I have built the proof of 2 new Primality tests for Fermat numbers. (Don't expect them to reduce the time needed by the Pepin' test ...) Why posting a test for Fermat numbers here ? Because it is a first step in a more global work I'm working on dealing with Lucas Sequences. I hope I will be able in the future to provide new useful theorems (and probably new conjectures) dealing with Mersenne and Fermat numbers. Think about my guess at the end of the document, dealing with what I call "fixed point". I've asked xyzzy (administrator) to host my document (.pdf) and to provide the link in this thread. Just wait xyzzy is available. Thanks xyzzy. Let me know if my proof is correct ... Tony 
20040910, 21:15  #2 
Feb 2004
France
2^{4}×59 Posts 
The .pdf file is attached to this post.
Hi, Finally, the .pdf file is attached to this post. Tony

20040911, 07:26  #3 
Feb 2004
France
2^{4}·59 Posts 
Second version about Pepin's test
Hi,
I've done 3 small modifications: 1) page 1 in the introduction: I say this also proves the Pepin's Test, with k=3 . 2) page 2 I've replaced the use of Pepin's test by the Euler congruence for quadratic residues. 3) page 4 I show that the Theorem 1 does prove the Pepin's test for k=3 . Tony 
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