20100503, 14:04  #12 
Mar 2009
26_{16} Posts 
Although English is not my native langage, I think your Proposition 1:
Code:
If M_p is not prime, when this is true: phi(M_p) = 0 mod p^2 Code:
If M_p is not prime, then this is true: phi(M_p) = 0 mod p^2. 
20100503, 14:25  #13  
"Bob Silverman"
Nov 2003
North of Boston
2^{2}×1,877 Posts 
Quote:
Given N = 2^p1, and N is composite then N is the product of at least two primes, each of which is 1 mod p. phi(N) will be divisible by p^k, where k is the number of distinct prime factors of N. This does not merit calling it a 'conjecture'. It is an elementary homework problem that one might assign to a beginning number theory class. 

20100507, 06:08  #14  
Jan 2010
germany
2·13 Posts 
Quote:


20100507, 11:09  #15  
"Bob Silverman"
Nov 2003
North of Boston
2^{2}×1,877 Posts 
Quote:
Look up "Wieferich" 

20100508, 00:33  #16 
"Richard B. Woods"
Aug 2002
Wisconsin USA
2^{2}×3×641 Posts 
Also, Mathworld (http://mathworld.wolfram.com/) is your mathematical friend, usually.
http://mathworld.wolfram.com/search/...erich&x=10&y=9 
Thread Tools  
Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
New Mersenne Conjecture  ATH  Math  28  20210805 05:50 
Use of new Mersenne conjecture ?  bhelmes  Number Theory Discussion Group  0  20170728 20:34 
conjecture about mersenne numbers  sascha77  Math  2  20100107 08:06 
The New Mersenne Conjecture  Dougy  Math  32  20081026 07:17 
New Mersenne and Cunningham conjecture  olivier_latinne  Math  54  20080312 10:04 