[23] **viXra:1809.0600 [pdf]**
*submitted on 2018-09-30 07:35:40*

**Authors:** Colin James III

**Comments:** 1 Page. © Copyright 2018 by Colin James III All rights reserved. Respond to the author by email at: info@ersatz-systems dot com.

The totherian set definition is not tautologous.

**Category:** Number Theory

[22] **viXra:1809.0576 [pdf]**
*submitted on 2018-09-30 02:18:20*

**Authors:** Bado Idriss Olivier

**Comments:** 4 Pages.

The purpose of this article is to introduce the theory of totherian analysis in order to provide proof of the Riemann hypothesis: the concepts introduced have been so effective and we can use it to build a coherent and tangible analysis. Totherian analysis can be considered as an effective remedy in solving a lot of problems in mathematics

**Category:** Number Theory

[21] **viXra:1809.0571 [pdf]**
*submitted on 2018-09-28 08:11:33*

**Authors:** Victor Sorokine

**Comments:** 2 Pages.

If we leave only the last digits A', B', C' in the numbers A, B, C, then the third digit in the left
part of one of the equivalent Fermat’s equations will be greater than 1. And the inclusion of
the following digits in the numbers A, B, C can reduce the value of this digit only by 1.

**Category:** Number Theory

[20] **viXra:1809.0570 [pdf]**
*submitted on 2018-09-28 08:12:33*

**Authors:** Victor Sorokine

**Comments:** 1 Page. Russian version

Если в числах A, B, C оставить лишь последние цифры A', B', C', то третья цифра в
левой части одного из эквивалентных равенств Ферма будет больше 1. А включение в
числа A, B, C последующих цифр могут уменьшить значение этой цифры лишь на 1.

**Category:** Number Theory

[19] **viXra:1809.0554 [pdf]**
*submitted on 2018-09-29 05:26:24*

**Authors:** Bado Idriss Olivier

**Comments:** 6 Pages.

The purpose of this article is to introduce the theory of totherian analysis in order to provide proof of the Riemann hypothesis: the concepts introduced have been so effective and we can use it to build a coherent and tangible analysis. Totherian analysis can be considered as an effective remedy in solving a lot of problems in mathematics

**Category:** Number Theory

[18] **viXra:1809.0522 [pdf]**
*submitted on 2018-09-25 13:29:51*

**Authors:** Colin James III

**Comments:** 1 Page. © Copyright 2016, 2018 by Colin James III All rights reserved. Respond to the author by email at: info@ersatz-systems dot com.

Conjecture sentence "If p or q is equivalent to s and p,q,s are relatively prime, then p or q is tautologous" is not tautologous, and it deviates by one value: FTTT TTTT TTTT TTTT.

**Category:** Number Theory

[17] **viXra:1809.0514 [pdf]**
*submitted on 2018-09-24 07:49:36*

**Authors:** Edgar Valdebenito

**Comments:** 4 Pages.

This note presents an integral for Catalan's constant.

**Category:** Number Theory

[16] **viXra:1809.0505 [pdf]**
*submitted on 2018-09-24 13:03:16*

**Authors:** Joseph Dise

**Comments:** 2 Pages.

A short demonstration of the title claim, which proves the Legendre conjecture and potentially other conjectures.

**Category:** Number Theory

[15] **viXra:1809.0503 [pdf]**
*submitted on 2018-09-24 16:12:05*

**Authors:** Abdelmajid Ben Hadj Salem

**Comments:** 4 Pages. Comments welcome.

We give an elementary proof of the ABC conjecture.

**Category:** Number Theory

[14] **viXra:1809.0488 [pdf]**
*replaced on 2018-10-15 13:52:47*

**Authors:** Emmanuil Manousos

**Comments:** 35 Pages.

It holds that every product of natural numbers can also be written as a sum. The inverse does not hold when 1 is excluded from the product. For this reason, the investigation of natural numbers should be done through their sum and not through their product. Such an investigation is presented in the present article. We prove that primes play the same role for odd numbers as the powers of 2 for even numbers, and vice versa. The following theorem is proven: “Every natural number, except for 0 and 1, can be uniquely written as a linear combination of consecutive powers of 2 with the coefficients of the linear combination being -1 or +1.” This theorem reveals a set of symmetries in the internal order of natural numbers which cannot be derived when studying natural numbers on the basis of the product. From such a symmetry a method for identifying large prime numbers is derived. We prove a factorization test for the natural numbers.

**Category:** Number Theory

[13] **viXra:1809.0479 [pdf]**
*submitted on 2018-09-22 05:35:56*

**Authors:** Nicolò Rigamonti

**Comments:** 4 Pages.

In this paper we will resume and conclude the last work.

**Category:** Number Theory

[12] **viXra:1809.0449 [pdf]**
*submitted on 2018-09-20 16:53:30*

**Authors:** Juan Moreno Borrallo

**Comments:** 5 Pages. (Spanish version)

In this paper it is demonstrated Fermat's last theorem only using elementary methods.

**Category:** Number Theory

[11] **viXra:1809.0351 [pdf]**
*submitted on 2018-09-17 17:16:10*

**Authors:** S.I. Nada, A. Elrokh, R. Hamza

**Comments:** 16 pages

Abstract
A graph is called cordial if it has a 0 - 1 labeling such that the number
of vertices (edges) labeled with ones and zeros dier by at most one. The
conjunction of two graphs (V1;E1) and (V2;E2) is the graph G = (V;E),
where V = V1 x V2 and u = (a1; a2), v = (b1; b2) are two vertices, then
uv belongs to E if aibi belongs to Ei for i = 1 or 2. In this paper, we present necessary and
sucient condition for cordial labeling for the conjunction of two paths,
denoted by Pn ^ Pm. Also, we drive an algorithm to generate cordial labeling for the conjunction Pn ^ Pm.

**Category:** Number Theory

[10] **viXra:1809.0341 [pdf]**
*submitted on 2018-09-16 11:10:33*

**Authors:** Pablo Hernan Pereyra

**Comments:** 8 Pages. Copyright 2007

In the present work is demonstrate that the so called Goldbach conjecture from 1742 -- “All positive even numbers greater than two can be expressed as a sum of two primes” – due to Leonhard Euler, is a true statement. This result is partially based on the Wilson theorem, and complementary on our reasoning to cast the problem into a diophantine equation. The latter is the master equation for the conjectures proof.

**Category:** Number Theory

[9] **viXra:1809.0338 [pdf]**
*submitted on 2018-09-16 13:40:39*

**Authors:** Paco Derek Tucker

**Comments:** 1 Page.

A simple and fast factoring algorithm that requires only copy paste, the modular operation, and paired additive partitions of the number.

**Category:** Number Theory

[8] **viXra:1809.0322 [pdf]**
*submitted on 2018-09-15 10:35:14*

**Authors:** Hajime Mashima

**Comments:** 9 Pages.

Legendre's conjecture argues that there is always a prime number between n2 and (n + 1)2 when natural number n.

**Category:** Number Theory

[7] **viXra:1809.0207 [pdf]**
*submitted on 2018-09-10 14:02:28*

**Authors:** Samia Lakehal

**Comments:** 13 Pages ; 2 Tables ; 766 Ko

The Sieve of Eratosthenes finds all the prime numbers up to any given limit by eliminating all non-primes from the list of all natural numbers. A list of natural numbers containing no multiples of 2, 3 or 5 is created, it is obtained by 8 formulas. The elimination of non-primes is effectuated from this new list. It then appears that it is possible to express all the non-primes belonging to this list by 36 other formulas, the prime numbers being the numbers satisfying the 8 formulas but not the 36.

**Category:** Number Theory

[6] **viXra:1809.0158 [pdf]**
*submitted on 2018-09-07 14:10:16*

**Authors:** Robert C. Hall

**Comments:** 27 Pages.

The Summation test consists of adding all numbers that begin with a particular first digit or first two digits and determining its distribution with respect to these first or first two digits numbers. Most people familiar with this test believe that the distribution is a uniform distribution for any distribution that conforms to Benford's law i.e. the distribution of the mantissas of the logarithm of the data set is uniform U[0,12). The summation test that results in a uniform distribution is true for an exponential function (geometric progression) but not true for a data set that conforms to a Log Normal distribution even when the Log Normal distribution itself closely approximates Benford's Law.

**Category:** Number Theory

[5] **viXra:1809.0139 [pdf]**
*submitted on 2018-09-08 05:07:23*

**Authors:** Ryujin Choe

**Comments:** 1 Page.

Solution of Goldbach's Conjecture

**Category:** Number Theory

[4] **viXra:1809.0086 [pdf]**
*submitted on 2018-09-04 16:35:05*

**Authors:** Kunle Adegoke

**Comments:** 7 pages, no figures

We derive an identity connecting any two Horadam sequences having the same recurrence relation but whose initial terms may be different. Binomial and ordinary summation identities arising from the identity are developed.

**Category:** Number Theory

[3] **viXra:1809.0060 [pdf]**
*submitted on 2018-09-03 15:11:34*

**Authors:** Pablo Hernan Pereyra

**Comments:** 5 Pages. 2009 Copyright

This paper aims to present an elementary demonstration of the Fermat-Wiles theorem, also known as Fermat's Last Theorem, using a different equivalent statement and a parameterization method.

**Category:** Number Theory

[2] **viXra:1809.0059 [pdf]**
*submitted on 2018-09-03 20:40:44*

**Authors:** Jeozadaque Marcos

**Comments:** 4 pages

We show in this paper another proof of Benford’s Law. The idea starts with the
problem of to find the first digit of a power. Then we deduced a function to calculate
the first digit of any power a j called L f function. The theorem 1.2 its a consequence
of the periodicity of the $L_f$ function.

**Category:** Number Theory

[1] **viXra:1809.0008 [pdf]**
*submitted on 2018-09-01 03:59:30*

**Authors:** Radomir Majkic

**Comments:** 3 Pages.

The minimal homothetic integer solution of the Fermat equation is zero and the Fermat last theorem is true.

**Category:** Number Theory