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Old 2005-09-11, 19:50   #12
cyrix
 
Jul 2003
Thuringia; Germany

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Quote:
Originally Posted by T.Rex
About q=53 I don't understand how 1 statement is true (5^...) though the other one is false (R^2+R-1 ...) since they are related. Do you ?
These two statements are related, yes. But the 5^... is stronger, because it uses the litte Fermat, too.

For q=53 the number 5 is a quadratic residue, but M_q does not hold a fermat-test with base 5.

Cyrix

Last fiddled with by cyrix on 2005-09-11 at 19:51
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Old 2005-09-12, 07:56   #13
T.Rex
 
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Feb 2004
France

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Default P้pin's test proved by means of LLT means

Hi Cyrix,
About what I said about proving that a P้pin's-like 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 P้pin'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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