20100107, 08:13  #1 
Jan 2010
germany
2×13 Posts 
Mersenne Conjecture
Hello,
My conjecture is : Let be an Mersennenumber, and a is an element from (1) > (2) This means, that if (1) is true, than is (2) also true. It is easy to show that ? My idea to do this with is prime, was the following: When is prime, when the Elements with the form are the only ones, that have order of and therefore:  But the only solution to this is 1: > > So can not be the order of a, because a is 1. I have searched with google many sites, but could not find the answer to this "problem". I hope that anybody can help me with the conjecture. kind regards, sascha 
20100107, 18:28  #2 
Feb 2005
2^{2}×3^{2}×7 Posts 
(1) implies (2) for all if and only if does not divide .
In other words, you need to prove either of the two statements: * if is Wieferich prime then is not prime; * if is prime then is not a Wieferich prime. It may be hard to prove. 
20100108, 08:44  #3 
Jan 2010
germany
2×13 Posts 
Thanks maxal,
Now I see the connection to the Wieferich primes and I feel confident now that this is hard to solve. 
20100209, 04:58  #4 
Jan 2010
379 Posts 
Do you have a proof to this conjecture (without inclding the 2^{p}1 prime number option)?

20100209, 05:29  #5 
Undefined
"The unspeakable one"
Jun 2006
My evil lair
3·7·13·23 Posts 

20100209, 19:17  #6 
Jan 2010
573_{8} Posts 
What do you mean by element ( I tought element is a member in a set).
Do you have an example for an element of a merssene number? 
20100209, 20:31  #7  
Nov 2003
2^{2}×5×373 Posts 
Quote:
units of Z/(2^p1)Z , i.e. an element of its maximal cyclic subgroup. 

20100209, 20:47  #8 
Jan 2010
17B_{16} Posts 
Silverman,
So he just mean a factor of 2^{p}1. BTW: I started reading "solved and unsloved problems in mathematics", I really enjoy it and it is really readable for my level. 
20100210, 07:34  #9  
Just call me Henry
"David"
Sep 2007
Cambridge (GMT/BST)
3^{4}×73 Posts 
Quote:
Are you learning from it or just enjoying it? Might get it myself 

20100210, 16:30  #10 
Jan 2010
379 Posts 
Henry,
I do read it, it isn't easy and it takes me time to understand. When I say "enjoy", I mean that it is really fun for me to learn more mathematics, I love mathematics, so why won't I enjoy reading a math book? I'm not going to read a book if I'm going to be bored of it.. 
20100425, 23:31  #11 
Jan 2010
germany
2×13 Posts 
Explanation of my conjecture.
Hello ,
I wrote an PDFdocument to show why I am interested that "my" conjecture is true. Sorry that it took so long time ;( In this PDF there might be some "new" Mersenne Properties, but I am not really shure if they are not well known. So I post this document here, in hope that the information might be usefull for someone. If I did mathematical mistakes in the document I would really be glad if you can say what I did false. ( I know there are plenty of englishgrammarmistakes ;) Please excuse my bad english) kind regards, Sascha Last fiddled with by sascha77 on 20100425 at 23:47 
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