A property of prime Mersenne numbers under LLT - Page 2

cyrix · 2005-09-11, 19:50

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

T.Rex · 2005-09-12, 07:56

Hi Cyrix,
About what I said about proving that a P�pin'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 P�pin'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

2005-09-12, 07:56	#13
T.Rex Feb 2004 France 2²·229 Posts	P�pin's test proved by means of LLT means Hi Cyrix, About what I said about proving that a P�pin'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 P�pin'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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