20050911, 19:50  #12  
Jul 2003
Thuringia; Germany
72_{8} Posts 
Quote:
For q=53 the number 5 is a quadratic residue, but M_q does not hold a fermattest with base 5. Cyrix Last fiddled with by cyrix on 20050911 at 19:51 

20050912, 07:56  #13 
Feb 2004
France
1622_{8} Posts 
Pépin's test proved by means of LLT means
Hi Cyrix,
About what I said about proving that a Pépin'slike test can be used for Mersenne numbers, look at the bottom of page 4 of this paper, which clearly shows that one can prove the Pépin's test (with k=3) for Fermat numbers by means of technics developped by Lucas and refined by Ribenboim for Mersenne numbers, and that I generalized and applied to Fermat numbers. So I guess the same could be done (with k=5) for Mersenne numbers. The problem is to find the appropriate Lucas Sequence, I think. Tony 
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