[10] **viXra:1905.0365 [pdf]**
*submitted on 2019-05-19 12:19:51*

**Authors:** Emmanuil Manousos

**Comments:** 20 Pages.

“Every natural number, with the exception of 0 and 1, can be written in a unique way as a linear combination of consecutive powers of 2, with the coefficients of the linear combination being -1 or +1”. According to this theorem we define the L/R symmetry of the natural numbers. The L/R symmetry gives the factors which determine the internal structure of natural numbers. As a consequence of this structure, we have an algorithm for determining prime numbers and for factorization of natural numbers.

**Category:** Number Theory

[9] **viXra:1905.0269 [pdf]**
*submitted on 2019-05-17 15:12:11*

**Authors:** Wilson Torres Ovejero

**Comments:** 16 Pages.

160 years ago that in the complex analysis a hypothesis was raised, which was used in principle
to demonstrate a theory about prime numbers, but, without any proof; with the passing Over the years, this
hypothesis has become very important, since it has multiple applications to physics, to number theory, statistics,
among others In this article I present a demonstration that I consider is the one that has been dodging all this
time.

**Category:** Number Theory

[8] **viXra:1905.0250 [pdf]**
*submitted on 2019-05-16 16:10:59*

**Authors:** Yuly Shipilevsky

**Comments:** 5 Pages.

We consider a new conjecture regarding powers of integer numbers and
more specifically, we are interesting in existence and finding pairs of integers:
n ≥ 2 and m ≥ 2, such that nm
= mn. We conjecture that n = 2, m = 4
and n = 4, m = 2 are the only integral solutions.
Next, we consider the corresponding generalizations for Hypercomplex
Integers: Gaussian and Lipschitz Integers.

**Category:** Number Theory

[7] **viXra:1905.0210 [pdf]**
*submitted on 2019-05-14 15:29:38*

**Authors:** Arthur Shevenyonov

**Comments:** 6 Pages. trilinear

A set of minimalist demonstrations suggest how the key premises of RH may have been inspired and could be qualified, by proposing a linkage between the critical strip (0..n) and Re(s)=x-1/2 interior of candidate solutions. The solution density may be concentrated around the focal areas amid the lower and upper bound revealing rarefied or latent representations. The RH might overlook some of the ontological structure while confining search to phenomena while failing to distinguish between apparently concentrated versus seemingly non-distinct candidates.

**Category:** Number Theory

[6] **viXra:1905.0137 [pdf]**
*submitted on 2019-05-10 01:25:34*

**Authors:** Marko Jankovic

**Comments:** 11 Pages.

In this paper a proof of the existence of an infinite number of Sophie Germain primes, is going to be presented. In order to do that, we analyse the basic formula for prime numbers and decide when this formula would produce a Sophie Germain prime, and when not. Originally very difficult problem (in observational space) has been transformed into a simpler one (in generative space) that can be solved by elementary math.

**Category:** Number Theory

[5] **viXra:1905.0111 [pdf]**
*replaced on 2019-05-11 18:48:26*

**Authors:** Toshiro Takami

**Comments:** 62 Pages.

new version
I believe this is proof of the Riemann hypothrsis.
I could give a complete proof by the number theory method to Riemann hypothesis.
I found the following number law. This proved that Riemann hypothesis is correct.

**Category:** Number Theory

[4] **viXra:1905.0098 [pdf]**
*submitted on 2019-05-06 16:48:48*

**Authors:** Zeolla Gabriel Martín

**Comments:** 7 Pages.

This document develops and demonstrates the discovery of a new cubic potentiation algorithm that works absolutely with all the numbers using the formula of the cubic of a binomial.

**Category:** Number Theory

[3] **viXra:1905.0041 [pdf]**
*submitted on 2019-05-02 12:38:19*

**Authors:** Abdelmajid Ben Hadj Salem

**Comments:** 9 Pages. Submitted to the journal Monatshefte für Mathematik. Comments welcome.

In this paper, we consider the abc conjecture in the case c=a+1. Firstly, we give the proof of the first conjecture that c

**Category:** Number Theory

[2] **viXra:1905.0021 [pdf]**
*submitted on 2019-05-01 08:54:31*

**Authors:** Timothy W. Jones

**Comments:** 3 Pages.

This is an easy approach to proving zeta(2) is irrational. The reasoning is by analogy with gym weights that are rational proportions of a unit. Sometimes the sum of such weights is expressible as a multiple of a single term in the sum and sometimes it isn't. The partials of zeta(2) are of the latter type. We use a result of real analysis and this fact to show the infinite sum has this same property and hence is irrational.

**Category:** Number Theory

[1] **viXra:1905.0010 [pdf]**
*submitted on 2019-05-01 18:09:11*

**Authors:** Yuly Shipilevsky

**Comments:** 7 Pages.

We introduce a special class of complex numbers, wherein their
absolute values and arguments given in a polar coordinate system are integers,
which when considered within the complex plane, constitute Unicentered
Radial Lattice and similarly for quaternions.

**Category:** Number Theory