[26] **viXra:1811.0503 [pdf]**
*submitted on 2018-11-29 17:48:12*

**Authors:** Zhang Tianshu

**Comments:** 18 Pages.

In this article, the author uses the mathematical induction, classifies positive integers gradually, and passes necessary operations by the operational rule to achieve finally the purpose proving Collatz conjecture.

**Category:** Number Theory

[25] **viXra:1811.0476 [pdf]**
*submitted on 2018-11-28 19:00:23*

**Authors:** Toshiro Takami

**Comments:** 9 Pages.

I found out
(√10a×1-1) (√10a×1+1)+20
(a is positive integer.)
is very effective of prime number production equation.

**Category:** Number Theory

[24] **viXra:1811.0471 [pdf]**
*submitted on 2018-11-29 00:56:11*

**Authors:** Divyendu Priyadarshi

**Comments:** 1 Page.

In this small paper , I have given a simple proof of
already well established fact that there are infinitely many prime numbers.

**Category:** Number Theory

[23] **viXra:1811.0459 [pdf]**
*submitted on 2018-11-27 10:05:16*

**Authors:** Victor Sorokine

**Comments:** 2 Pages.

he essence of the proof of the FLT:
The first case (ABC is not a multiple of n):
In one of the equivalent Fermat equations, the 3rd digit of the sum of the powers of the last digits of the bases greater than 1, which cannot be zeroed using the second digits with the sum of the latter equal to 0 or n-1.
+++
The second case (A or B or C is a multiple of n):
(k+2)-th digit in the number D=(A+B)^n-(C-B)^n-(C-A)^n, where the number A+B-C ends by k zeros, is not zero, but after adding to the number D zero as 0=A^n+B^n-C^n (k+2)-th digit is zero.

**Category:** Number Theory

[22] **viXra:1811.0457 [pdf]**
*submitted on 2018-11-27 10:06:38*

**Authors:** Victor Sorokine

**Comments:** 2 Pages. Russian version

Суть доказательства ВТФ:
Первый случай (ABC не кратно n):
В одном из эквивалентных равенств Ферма 3-я цифра суммы степеней последних цифр оснований больше 1, которую невозможно обнулить с помощью вторых цифр с суммой последних, равной 0 или n-1.
+++
Второй случай (A или B или C кратно n):
(k+2)-я цифра в числе D=(A+B)^n-(C-B)^n-(C-A)^n, где число A+B-C оканчивается на k нулей, не равна нулю, но после прибавления к числу D нуля в виде 0=A^n+B^n-C^n (k+2)-я цифра равна нулю.

**Category:** Number Theory

[21] **viXra:1811.0348 [pdf]**
*submitted on 2018-11-23 04:44:14*

**Authors:** Toshiro Takami

**Comments:** 10 Pages.

Last time, I expressed ζ (odd number), such as ζ(3), ζ (5), ζ(7), ζ(9), ζ(11), ζ(13), ζ (15), ζ(17), ζ (19), ζ (21), ζ(23) and made an official.
Another way of expressing ζ (odd number), such as ζ(3), ζ (5), ζ(7) ζ(9), ζ(11), ζ(13), ζ(15), ζ(17), ζ(19), ζ(21), ζ(23) and made an official.

**Category:** Number Theory

[20] **viXra:1811.0338 [pdf]**
*replaced on 2018-11-23 22:07:51*

**Authors:** Marco Ripà

**Comments:** 3 Pages.

We provide a preliminary proof of Ripà’s Conjecture 3 about the convergence speed of tetration, published in October 2018, which states that, for any natural number "v", exists (at least) another natural number "a", not a multiple of 10, such that V(a)=v, where V(a) represents the convergence speed of the tetration a^^b.

**Category:** Number Theory

[19] **viXra:1811.0320 [pdf]**
*submitted on 2018-11-20 09:10:58*

**Authors:** Zeolla Gabriel Martín

**Comments:** 9 Pages. English language

This paper develops a new multiplication algorithm that works absolutely with all the numbers.

**Category:** Number Theory

[18] **viXra:1811.0288 [pdf]**
*submitted on 2018-11-18 11:45:11*

**Authors:** Robert C. Hall

**Comments:** 20 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[0,1). The summation test that results in a uniform distribution is true for an exponential function (geometric progression) i.e. y = a exp(kt) but not necessarily true for other data sets that conform exactly to Benford'a law.

**Category:** Number Theory

[17] **viXra:1811.0282 [pdf]**
*submitted on 2018-11-18 21:44:13*

**Authors:** Stefan Bereza

**Comments:** 4 Pages.

Fermat's Last Theorem (FLT) x^p + y^p = z^p could be seen as a special case of more generalized Beal's Conjecture (BC) x^m + y^n = z^r. Those equations are impossible when x, y and z are natural numbers and coprimes and {p, m, n, r}> = 3; if m = n = r (= p), then it is FLT; if not, Beal's Conjecture.
In BC, if x, y and z are integers and have a common factor, they can be measured (without rest) with this factor as a common unit - making x, y and z in the equation rational to each other. FLT can be proved with proving irrationality of triangles inscribed into an ellipse whose sides x, y and z represent the Fermat's equation x^p + y^p = z^p ; here, for x, y and z a common unit cannot be found. The BC equation
x^m + y^n = z^r (without a common factor) can be simplified to the Fermat's equation x^p + y^p = z^p which - at the lacking common unit - makes x, y and z impossible to be all rational to each other.

**Category:** Number Theory

[16] **viXra:1811.0263 [pdf]**
*submitted on 2018-11-17 20:39:55*

**Authors:** Olivier Massot

**Comments:** 22 Pages.

The binomial formula, set by Isaac Newton, is of utmost importance and has been extensively used in many different fields. This study (in French) aims at coming up with alternative expressions to the Newton's formula.

**Category:** Number Theory

[15] **viXra:1811.0262 [pdf]**
*submitted on 2018-11-17 20:44:21*

**Authors:** Olivier Massot

**Comments:** 22 Pages.

The binomial formula, set by Isaac Newton, is of utmost importance and has been extensively used in many different fields. This study aims at coming up
with alternative expressions to the Newton's formula.

**Category:** Number Theory

[14] **viXra:1811.0250 [pdf]**
*submitted on 2018-11-16 11:08:43*

**Authors:** Abdelmajid Ben Hadj Salem

**Comments:** 6 Pages. Comments welcome.

In this paper, we give a proof minus $\epsilon$ of the $ABC$ conjecture, considering that Beal conjecture is true. Some conditions are proposed for the proof, perhaps it needs some justifications that is why I give the title of the paper " a proof minus $\epsilon$ of the $ABC$ conjecture".

**Category:** Number Theory

[13] **viXra:1811.0211 [pdf]**
*submitted on 2018-11-13 08:01:46*

**Authors:** Zeolla Gabriel Martín

**Comments:** 9 Pages. Idioma: Español

Este documento desarrolla y demuestra el descubrimiento de un nuevo algoritmo de multiplicación que funciona absolutamente con todos los números.

**Category:** Number Theory

[12] **viXra:1811.0179 [pdf]**
*submitted on 2018-11-11 19:03:33*

[11] **viXra:1811.0159 [pdf]**
*submitted on 2018-11-11 04:13:06*

**Authors:** Zach Don

**Comments:** 1 Page.

In this paper, I will be presenting an alternative way of writing the Riemann zeta function in terms of Euler's constant, e.

**Category:** Number Theory

[10] **viXra:1811.0158 [pdf]**
*submitted on 2018-11-11 04:19:06*

**Authors:** Zach Don

**Comments:** 1 Page.

In this paper, I will propose a legitimate way of re-writing the Riemann zeta function in terms of Euler's constant, e.

**Category:** Number Theory

[9] **viXra:1811.0119 [pdf]**
*submitted on 2018-11-07 10:57:26*

**Authors:** Viktor Strohm

**Comments:** 5 Pages.

In accordance with the General Theory Systems of Urmantsev (GTSU) [1, 2, 3], the set of primes is considered as a system of objects. For the relationship between objects taken the difference of prime numbers. Revealed periodicity of pairs of intervals.

**Category:** Number Theory

[8] **viXra:1811.0116 [pdf]**
*replaced on 2018-12-22 21:36:55*

**Authors:** Colin James III

**Comments:** 1 Page.

Properties of the zeta function of the Riemann hypothesis are not confirmed as tautologous and hence refute it.

**Category:** Number Theory

[7] **viXra:1811.0112 [pdf]**
*replaced on 2018-11-09 19:22:45*

**Authors:** Es-said En-naoui

**Comments:** 5 Pages.

The Goldbach conjecture dates back to 1742 ; we refer the reader to [1]-[2] for a history of the conjecture. Christian Goldbach stated that every odd integer greater than seven can be written as the sum of at most three prime numbers. Leonhard Euler then made a stronger conjecture that every even integer greater than four can be written as the sum of two primes. Since then, no one has been able to prove the Strong Goldbach Conjecture.\\
The only best known result so far is that of Chen [3], proving that every sufficiently large even integer N can be written as the sum of a prime number and the product of at most two prime numbers. Additionally, the conjecture has been verified to be true for all even integers up to $4.10^{18}$ in 2014 , J\"erg [4] and Tom\'as [5]. In this paper, we prove that the conjecture is true for all even integers greater than 8.

**Category:** Number Theory

[6] **viXra:1811.0080 [pdf]**
*replaced on 2019-03-14 14:04:51*

**Authors:** Ralf Wüsthofen

**Comments:** 1 Page.

This note proves the inconsistency of the Peano arithmetic (PA) by using a strengthened form of the strong Goldbach conjecture and its negation.

**Category:** Number Theory

[5] **viXra:1811.0072 [pdf]**
*replaced on 2019-01-01 23:58:16*

**Authors:** Quang Nguyen Van

**Comments:** 4 Pages.

We give a expression of w^n and the possible to apply for solving Fermat's Last theorem.

**Category:** Number Theory

[4] **viXra:1811.0046 [pdf]**
*submitted on 2018-11-03 21:04:42*

**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.

Karush-Kuhn-Tucker constraints for linear programming are not tautologous.

**Category:** Number Theory

[3] **viXra:1811.0032 [pdf]**
*replaced on 2019-04-13 07:50:24*

**Authors:** Hassine Saidane

**Comments:** 5 Pages.

Abstract. The optimization of theoretical concepts such as action or utility functions enabled the derivation of important theories and laws in some scientific fields such as physics and economics. These breakthroughs suggested that the problem of the location of the Riemann Zeta Function’s (RZF) nontrivial zeros can be similarly addressed in a mathematical programming framework. Using a constrained nonlinear optimization formulation of the problem, we prove that RZF’s nontrivial zeros are located on the critical line, thereby confirming the Riemann Hypothesis. This result is a direct implication of the Karush-Kuhn-Tucker optimality conditions associated with the formulated nonlinear program.
Keywords: Riemann Zeta function, Riemann Hypothesis, Constrained Optimization, Kuhn-Tucker conditions.

**Category:** Number Theory

[2] **viXra:1811.0017 [pdf]**
*submitted on 2018-11-01 12:03:50*

**Authors:** Salvatore Gerard Micheal

**Comments:** 2 Pages.

a brief exposition on quantifying irrational density within the reals - and - attempt to categorize groups of irrationals

**Category:** Number Theory

[1] **viXra:1811.0016 [pdf]**
*submitted on 2018-11-01 12:17:02*

**Authors:** Clemens Kroll

**Comments:** 6 Pages.

It is shown that Riemann’s hypothesis is true by showing that an equivalent statement is true. Even more, it is shown that Stieltjes’ conjecture is true.

**Category:** Number Theory