20040602, 05:27  #1 
May 2004
2^{2}×79 Posts 
Fermat,s Theorem
There are several ways of generalising F.T.:
1) Euler's 2) Gauss's 3) Devaraj's (ref: www.crorepatibaniye.com\failurefunctions 4) Euler's gen. of F.T.a further gen (ref site above) Is there any other way? Looking forward to replies Sincerely Devaraj Last fiddled with by devarajkandadai on 20040602 at 05:30 
20040602, 15:25  #2 
∂^{2}ω=0
Sep 2002
República de California
11,399 Posts 
You need to change the Windowsstyle \ in your link to a / so most browsers can properly handle it.
I glanced at the page about the proposed generalization of Fermat's theorem. First off, could you please provide some concrete examples? For instance, use your algorithm to find any factor of a small knowncomposite Fermat number. Also, you examine numbers of the form f(x) = a^x + c, where a and x are natural and c integer. But your approach seems to require a known value of x for which f is prime  testing primality for any single value of x is of course subexponential in terms of labor, but you don't say anything about the feasibility of finding such an x  if one or more such x exists, how many trials might be needed to find it? In other words, for functions f which admit such x, how many such x will there be on average? 
20040603, 10:00  #3  
May 2004
2^{2}×79 Posts 
Fermat's Theorem
Thank u for your tip regarding slashes.
This thread is about possible ways of generalising Fermat's Thorem. As you are aware the textbooks mention Euler's and Gauss's ways.The other two are on my site.I thought for the sake of easy understanding by all members of the group I will begin with the concept of failure functions and develop the logical thread till we reach the practical applications.Incidentally my paper "Euler's Generalisation of Fermat's Theorem a further generalisation" is being presented by me at Hawaii Intl. Conference on Statistics, Maths & related fields (912 June) Is my proposal o.k. with you?Regards Devaraj Quote:


20040605, 10:15  #4 
May 2004
2^{2}×79 Posts 
Fermat's Theorem
This is with reference to Dr. Meyer's poser regarding possibility of using my theorm for fatorising Fermat numbers:
Both relevant papers on my site: www.crorepatibaniye.com/failurefunctions have algorithms in mathematical language.This has to be converted into Computer algorithms before the problem can be tackled.However my knowledge of computer programming is NIL.Regards Devaraj Last fiddled with by devarajkandadai on 20040605 at 10:16 
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