# Number Theory

## 1210 Submissions

 viXra:1210.0167 [pdf] replaced on 2013-02-23 09:25:37

### The Connection Between the Riemann Hypothesis and Model Theory.

Authors: Cristian Dumitrescu

In this paper, I present a connection between the Riemann Hypothesis and model theory, and this connection leads to a solution to the Riemann Hypothesis.
Category: Number Theory

 viXra:1210.0157 [pdf] submitted on 2012-10-27 01:10:44

### Prime Coordinates on a Modulo Map, and Sine Representation

Authors: Diego Alonso Cortez

We compute the primes up to 1 million by starting an arithmetic progression at every positive integer 2n, that grows by n, where n > 1. All numbers not in the progression are prime.
Category: Number Theory

 viXra:1210.0148 [pdf] replaced on 2014-09-17 10:43:16

### The Existence Of The Twin Primes

Authors: Bertrand Wong

The author had published a paper on the solutions for the twin primes conjecture in an international mathematics journal in 2003. This paper approaches the twin primes problem through the analysis of the intrinsic nature of the prime numbers.
Category: Number Theory

 viXra:1210.0147 [pdf] replaced on 2014-09-18 12:08:54

### The Infinity Of The Twin Primes

Authors: Bertrand Wong

The author had published a paper on the solutions for the twin primes conjecture in an international mathematics journal in 2003. This paper approaches the twin primes problem through the analysis of the composite numbers.
Category: Number Theory

 viXra:1210.0140 [pdf] replaced on 2012-10-25 10:11:22

### A Proof of the Lonely Runner Conjecture for Any n, with Rational Values Approximating Any Set of Arbitrary Integers with Infinite Precision

Authors: Patrick A Devlin

In number theory, and especially the study of the diophantine approximation, the Lonely Runner Conjecture is a conjecture with important and widespread applications in mathematics. A previous paper by this author proved the lonely runner conjecture for any n, for the special case of integers with particularly correlated prime factors. In this paper we attempt to extend this work to the general case of n arbitrary integers. The paper demonstrates that a set of integers with correctly correlated prime factors, such that they satisfy the conjecture, can be modified to approximate any set of arbitrary integers with infinite precision.
Category: Number Theory

 viXra:1210.0125 [pdf] submitted on 2012-10-22 16:16:11

### More Properties in Goldbach’s Conjecture

Authors: C. G. Provatidis

This paper reveals that the reference function G(2n)=2n/(ln(n))^2 plays a significant role in the distribution of the total number of pairs (p, q) of primes that fulfill the condition (p + q = 2n), which constitutes Goldbach’s conjecture. Numerical experiments up to 2n=500,000 show that, in the plot of the number of pairs versus 2n, the ratio of the lowest points over G(2n) tends asymptotically to the value 2/3. The latter fact dictates that the lower bound concerning the minimum number of pairs that fulfill Goldbach’s conjecture is equal to 4n/[3(ln(n))^2]. Moreover, smoothed sequences by treatment of the aforementioned pairs are revealed.
Category: Number Theory

 viXra:1210.0112 [pdf] replaced on 2012-10-25 09:56:10

### A Special Case of the Lonely Runner Conjecture for any n

Authors: Patrick A Devlin

In number theory, and especially the study of the diophantine approximation, the Lonely Runner Conjecture is a conjecture with important and widespread applications in mathematics. This paper attempts to prove the conjecture for any n runners in the special case of integers with particularly correlated prime factors.
Category: Number Theory

 viXra:1210.0066 [pdf] submitted on 2012-10-13 02:19:06

### Smoothening Properties Related to the Goldbach’s Conjecture

Authors: C. G. Provatidis

In this short paper we reveal a sequence of three smoothing procedures related to Goldbach’s conjecture. While the cloud of points that represent the number of pairs (p, q), which fulfill the conjecture p+q=2n, versus 2n occupies a quite broad area of curvilinear triangular shape, suitable averages can reduce it into oscillating lines with progressively decreasing amplitudes.
Category: Number Theory

 viXra:1210.0048 [pdf] submitted on 2012-10-10 02:57:48

### Fermat Proved His Last Theorem

Authors: Chun-Xuan Jiang

see paper for abstract in Chinese
Category: Number Theory

 viXra:1210.0027 [pdf] submitted on 2012-10-06 14:11:49

### The More Simple Proof of Fermat Last Theorem

Authors: Chun-Xuan Jiang

Category: Number Theory

 viXra:1210.0026 [pdf] submitted on 2012-10-06 10:36:09

### On the Resolution of the Riemann Hypothesis

Authors: Viktor K

In this paper, we present a resolution to the problem of the Riemann Hypothesis. In particular, by the use of the Mellin integral transform and analytic techniques, we prove there exist no zeros to the Riemann Zeta Function in the critical strip outside the line whose real component is 1/2.
Category: Number Theory

 viXra:1210.0017 [pdf] submitted on 2012-10-04 00:00:42

### The Answer to The Riemann Hypothesis - Chapter VII

Authors: Tian-Chou Wang
Comments: 69 Pages. Manuscript scan, in Chinese, and copyright belongs to the author.

This is a part of Dr. Tian-Chou Wang's proof to Riemann Hypothesis. It follows 'the opening' (viXra citation number: 1209.0063), Chapter 1 (viXra citation number: 1209.0068), Chapter 2 (viXra citation number: 1209.0078), Chapter 3 (viXra citation number: 1209.0090), Chapter 4 (viXra citation number: 1209.0100), Chapter 5 (viXra citation number: 1210.0008), Chapter 6 (viXra citation number: 1210.0013), and this is the end of Section One.
Category: Number Theory

 viXra:1210.0013 [pdf] submitted on 2012-10-02 20:57:43

### The Answer to The Riemann Hypothesis - Chapter VI

Authors: Tian-Chou Wang
Comments: 48 Pages. Manuscript scan, in Chinese, and copyright belongs to the author.

This is a part of Dr. Tian-Chou Wang's proof to the Riemann Hypothesis. It follows 'the opening' (viXra citation number: 1209.0063), Chapter 1 (viXra citation number: 1209.0068), Chapter 2 (viXra citation number: 1209.0078), Chapter 3 (viXra citation number: 1209.0090), Chapter 4 (viXra citation number: 1209.0100), Chapter 5 (viXra citation number: 1210.0008)
Category: Number Theory

 viXra:1210.0008 [pdf] submitted on 2012-10-01 19:09:51

### The Answer to The Riemann Hypothesis - Chapter V

Authors: Tian-Chou Wang
Comments: 51 Pages. Manuscript scan, in Chinese, and copyright belongs to the author.

This is a part of Dr. Tian-Chou Wang's proof to the Riemann Hypothesis. It follows 'the opening' (viXra citation number: 1209.0063), Chapter 1 (viXra citation number: 1209.0068), Chapter 2 (viXra citation number: 1209.0078), Chapter 3 (viXra citation number: 1209.0090), Chapter 4 (viXra citation number: 1209.0100)
Category: Number Theory