mersenneforum.org > Math Modified Fermat's theorem
 User Name Remember Me? Password
 Register FAQ Search Today's Posts Mark Forums Read

 2017-11-08, 03:45 #1 devarajkandadai     May 2004 22·79 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^2-1) = = 1 (mod p) where p is prime of shape 3m + 1 or 4m+3.
2017-11-10, 03:58   #2
devarajkandadai

May 2004

22·79 Posts

Quote:
 Originally Posted by devarajkandadai 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^2-1) = = 1 (mod p) where p is prime of shape 3m + 1 or 4m+3.
Of course a and p have to be coprime.

 2017-11-10, 11:33 #3 devarajkandadai     May 2004 22×79 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.
2017-11-12, 03:47   #4
devarajkandadai

May 2004

22×79 Posts

Quote:
 Originally Posted by devarajkandadai 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.
Mft works up to p = 89.Above this beyond pari(my version's capability ).

2017-11-12, 04:26   #5
CRGreathouse

Aug 2006

3·1,993 Posts

Quote:
 Originally Posted by devarajkandadai Mft works up to p = 89.Above this beyond pari(my version's capability ).
Really? Could you give an example of a calculation just beyond its ability?

 2017-11-12, 10:07 #6 bhelmes     Mar 2016 6208 Posts Perhaps this might be helpful for you: http://devalco.de/#104 Greetings from the primes Bernhard
2017-11-12, 11:23   #7
devarajkandadai

May 2004

22×79 Posts

Quote:
 Originally Posted by CRGreathouse Really? Could you give an example of a calculation just beyond its ability?
Sure: consider Mod(x,x^2+97). Let this be %1. You have to calculate ((2+%1)^(101^2-1)/101.
Thank you.

Last fiddled with by devarajkandadai on 2017-11-12 at 11:30 Reason: Typo

2017-11-12, 11:34   #8
science_man_88

"Forget I exist"
Jul 2009
Dumbassville

100000110000002 Posts

Quote:
 Originally Posted by devarajkandadai Sure: consider Mod(x,x^2+97). Let this be %1. You have to calculate ((2+%1)^(101^2-1)/101. Thank you.
no second ending parentheses on the other side of things ??

 2017-11-12, 15:39 #9 Dr Sardonicus     Feb 2017 Nowhere 22×1,459 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 non-zero ideal of R, and G = (R/I)x the multiplicative group of invertible elements mod I (which is finite).
2017-11-12, 16:50   #10
Batalov

"Serge"
Mar 2008
Phi(4,2^7658614+1)/2

23·32·137 Posts

Quote:
 Originally Posted by bhelmes Perhaps this might be helpful for you: http://devalco.de/#104 Greetings from the primes Bernhard
Mod warning: Another irrelevant plug for your webpages and you will receive a ban.

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!

2017-11-12, 17:09   #11
bhelmes

Mar 2016

24×52 Posts

Quote:
 Originally Posted by Batalov Mod warning: Another irrelevant plug for your webpages and you will receive a ban. 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".
As far as i understood the OP has tried to deal with a+bI ( a complex number) and a+b*sqrt (A) and the cycle construction concerning the primes

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

 Thread Tools

 Similar Threads Thread Thread Starter Forum Replies Last Post devarajkandadai Number Theory Discussion Group 12 2017-12-25 05:43 devarajkandadai Number Theory Discussion Group 1 2017-07-07 13:56 devarajkandadai Number Theory Discussion Group 0 2017-06-24 12:11 devarajkandadai Number Theory Discussion Group 2 2017-06-23 04:39 Citrix Math 24 2007-05-17 21:08

All times are UTC. The time now is 14:53.

Thu Jul 7 14:53:18 UTC 2022 up 9:40, 0 users, load averages: 1.28, 1.33, 1.29

Powered by vBulletin® Version 3.8.11
Copyright ©2000 - 2022, Jelsoft Enterprises Ltd.

This forum has received and complied with 0 (zero) government requests for information.

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation.
A copy of the license is included in the FAQ.

≠ ± ∓ ÷ × · − √ ‰ ⊗ ⊕ ⊖ ⊘ ⊙ ≤ ≥ ≦ ≧ ≨ ≩ ≺ ≻ ≼ ≽ ⊏ ⊐ ⊑ ⊒ ² ³ °
∠ ∟ ° ≅ ~ ‖ ⟂ ⫛
≡ ≜ ≈ ∝ ∞ ≪ ≫ ⌊⌋ ⌈⌉ ∘ ∏ ∐ ∑ ∧ ∨ ∩ ∪ ⨀ ⊕ ⊗ 𝖕 𝖖 𝖗 ⊲ ⊳
∅ ∖ ∁ ↦ ↣ ∩ ∪ ⊆ ⊂ ⊄ ⊊ ⊇ ⊃ ⊅ ⊋ ⊖ ∈ ∉ ∋ ∌ ℕ ℤ ℚ ℝ ℂ ℵ ℶ ℷ ℸ 𝓟
¬ ∨ ∧ ⊕ → ← ⇒ ⇐ ⇔ ∀ ∃ ∄ ∴ ∵ ⊤ ⊥ ⊢ ⊨ ⫤ ⊣ … ⋯ ⋮ ⋰ ⋱
∫ ∬ ∭ ∮ ∯ ∰ ∇ ∆ δ ∂ ℱ ℒ ℓ
𝛢𝛼 𝛣𝛽 𝛤𝛾 𝛥𝛿 𝛦𝜀𝜖 𝛧𝜁 𝛨𝜂 𝛩𝜃𝜗 𝛪𝜄 𝛫𝜅 𝛬𝜆 𝛭𝜇 𝛮𝜈 𝛯𝜉 𝛰𝜊 𝛱𝜋 𝛲𝜌 𝛴𝜎𝜍 𝛵𝜏 𝛶𝜐 𝛷𝜙𝜑 𝛸𝜒 𝛹𝜓 𝛺𝜔