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Old 2004-06-02, 05:27   #1
devarajkandadai
 
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May 2004

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Smile 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 2004-06-02 at 05:30
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Old 2004-06-02, 15:25   #2
ewmayer
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You need to change the Windows-style \ 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 known-composite 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?
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Old 2004-06-03, 10:00   #3
devarajkandadai
 
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Default 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 text-books 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 (9-12 June) Is my proposal o.k. with you?Regards
Devaraj
Quote:
Originally Posted by ewmayer
You need to change the Windows-style \ 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 known-composite 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?
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Old 2004-06-05, 10:15   #4
devarajkandadai
 
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May 2004

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Default 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 2004-06-05 at 10:16
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