20171108, 03:45  #1 
May 2004
2^{2}·79 Posts 
Modified Fermat's theorem
Works when the base is a Gausian integer as well as Z + Z*I*sqroot(7). Members may recall that Modified Fermat's theorem as a^(p^21) = = 1 (mod p) where p is
prime of shape 3m + 1 or 4m+3. 
20171110, 03:58  #2 
May 2004
2^{2}×79 Posts 

20171110, 11:33  #3 
May 2004
2^{2}·79 Posts 
Modified Fermat's theorem
This has been practically proved for Gaussian integer and bases a + b*sqrt(5).
see (Hardy's intro to number theory and Pollard's intro to algebraic number theory.For the rest of quadratic algebraic integers I do not know about proofs.However I can, with the help of pari, say what it works for. In my next post will give a few for which this conjecture seems to be valid. 
20171112, 03:47  #4  
May 2004
2^{2}·79 Posts 
Quote:


20171112, 04:26  #5 
Aug 2006
5987_{10} Posts 

20171112, 10:07  #6 
Mar 2016
640_{8} Posts 

20171112, 11:23  #7  
May 2004
474_{8} Posts 
Quote:
Thank you. Last fiddled with by devarajkandadai on 20171112 at 11:30 Reason: Typo 

20171112, 11:34  #8 
"Forget I exist"
Jul 2009
Dartmouth NS
20E2_{16} Posts 

20171112, 15:39  #9 
Feb 2017
Nowhere
1011111010101_{2} Posts 
The obvious "generalization of Fermat's theorem" is the generalization of Euler's theorem to number fields. This, in turn, is a special case of the result that, if G is a finite group, g is an element of G, and G the number of elements in G, then g^{G} = 1, the identity of G. This is a consequence of Lagrange's theorem, applied to the cyclic group generated by g. The application to number fields is, R is the ring of algebraic integers of a number field K, I is a nonzero ideal of R, and G = (R/I)^{x} the multiplicative group of invertible elements mod I (which is finite).

20171112, 16:50  #10  
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
7·1,427 Posts 
Quote:
What the heck does it even have to do with the topic of this thread, huh?! You just go from thread to thread and spam with "your website". Greetings from the composites! Have a nice day! 

20171112, 17:09  #11  
Mar 2016
2^{5}·13 Posts 
Quote:
In the given link you find a detailled version to the different cycle construction. This was a gentle and completely correct mathematic link. Besides you will not find this detailled information some where else. The link i have given is a part of nice mathematic and programmed skill. It is not nice to shoot with big guns, without any reason. By the way, i have dealt since some times with primes, and i have spent a lot of work to give a clear information about some prime topics on my website. You do not seem to appriciate my own work. Primes are very beautiful flowers Greetings from the primes Bernhard 

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