Number Theory

1202 Submissions

[8] viXra:1202.0086 [pdf] replaced on 2012-03-03 23:45:52

Controversy Between Jiang Proof and Wiles Proof for Fermat Last Theorem in China

Authors: Song Wen Miao
Comments: 3 Pages. CHINESE

ALL EYES ARE ON FERMAT LAST THEOREM WHO PROVED FORST
Category: Number Theory

[7] viXra:1202.0085 [pdf] submitted on 2012-02-28 04:04:30

Generalized Fermat Primes P Such that 3 is a Primitive Root Modulo P

Authors: Predrag Terzich
Comments: 4 Pages.

We explore some properties of generalized Fermat primes of the form : F_n(2q)=(2q)^(2^n)+1 , where n > 1 and q is an odd prime number .
Category: Number Theory

[6] viXra:1202.0067 [pdf] submitted on 2012-02-19 15:28:34

Proof of Legendre's and Brocard's Conjectures

Authors: Carlos Giraldo Ospina
Comments: 2 Pages.

In this paper Legendre’s Conjecture and Brocard’s Conjecture are proved by determining the amount of prime numbers that are located between N^2 and (N+1)^2.
Category: Number Theory

[5] viXra:1202.0063 [pdf] submitted on 2012-02-18 19:13:46

Infinitely Many Prime Numbers of the Form Ap±b

Authors: Germán Paz
Comments: 32 Pages, 15 pages of tables. On the tables that appear from pages 8 to 22, the numbers that are located on the third column and have commas should rather have dots, since this work is written in English. This detail does not change results at all.

In this paper it is proved that if 'a' and 'b' are two positive integers which are coprime and also have different parity, then there are infinitely many prime numbers of the form ap + b (where 'p' is a prime number) and infinitely many prime numbers of the form ap - b. In particular, all this proves that there are infinitely many prime numbers of the form 2p + 1, which proves there are infinitely many Sophie Germain Prime Numbers. This document also contains Lic. Carlos Giraldo Ospina's solution to the Polignac's Conjecture and to the Twin Prime Conjecture, which is one of Landau's Problems. Previous papers (written in Spanish language) were reviewed and approved by Lic. C. G. Ospina and versions of those papers were posted by this person on his own website and on ABCdatos. You may search for the papers' titles on the internet. You may also visit the websites that are mentioned in this paper. This work was submitted to the Journal of Number Theory.
Category: Number Theory

[4] viXra:1202.0061 [pdf] submitted on 2012-02-18 21:49:14

Solution to One of Landau's Problems

Authors: Germán Paz
Comments: 19 Pages. This paper was submitted to the Journal of Number Theory.

In this paper it is proved that for every positive integer 'k' there are infinitely many prime numbers of the form n^2+k. As a result, it is proved that there are infinitely many prime numbers of the form n^2+1. This document also proposes a new and important conjecture about prime numbers called 'Conjecture C'. If this conjecture is true, then Legendre’s Conjecture, Brocard’s Conjecture and Andrica’s Conjecture are all true, and also some other important results will be true. Previous papers (written in Spanish language) were reviewed and approved by Carlos Giraldo Ospina (Lic. Matemáticas, USC, Cali, Colombia). This person posted versions of these papers at his own personal website and at ABCdatos. You may search for those papers on the internet. You may also visit the websites that are mentioned in this paper.
Category: Number Theory

[3] viXra:1202.0056 [pdf] submitted on 2012-02-17 10:43:30

Fermat's Marvelous Proofs for Fermat Last Theorem

Authors: Chun-Xuan Jiang
Comments: 6 Pages.

Using cmplex hyperbolic functions and complex trionometric functions ,we reapear the Fermat marvelus proofs for Fermat last theorem
Category: Number Theory

[2] viXra:1202.0029 [pdf] replaced on 2014-08-25 05:42:42

Primality Test for Fermat Numbers Using Quartic Recurrence Equation

Authors: Predrag Terzich
Comments: 5 Pages.

We present deterministic primality test for Fermat numbers . Essentially this test is similar to the Lucas-Lehmer primality test for Mersenne numbers
Category: Number Theory

[1] viXra:1202.0024 [pdf] submitted on 2012-02-10 06:54:39

On the Form of Mersenne Numbers

Authors: Predrag Terzich
Comments: 4 Pages.

We present a theorem concerning the form of Mersenne numbers . We also discuss a closed form expression which links prime numbers and natural logarithms .
Category: Number Theory