Number Theory

2011 Submissions

[18] viXra:2011.0212 [pdf] submitted on 2020-11-30 13:34:29

Assuming C Less Then Rad2 (Abc), a New Proof of the Abc Conjecture

Authors: Abdelmajid Ben Hadj Salem
Comments: Pages.

In this paper, we consider the abc conjecture. Assuming that c<rad^2(abc) is true, we give a new proof of the abc conjecture, by proceeding with the contradiction of the definition of the abc conjecture, for \epsilon \geq 1, then for \epsilon \in ]0,1[.
Category: Number Theory

[17] viXra:2011.0207 [pdf] submitted on 2020-11-30 09:13:59

Goldbach’s Conjecture Algorithm Addendum

Authors: Elizabeth Gatton-Robey
Comments: 7 Pages. [Corrections made by viXra Admin to conform with the requirements on the Submission Form]

This is an addendum to the work I previously submitted at https://vixra.org/abs/1904.0227
Category: Number Theory

[16] viXra:2011.0206 [pdf] submitted on 2020-11-30 09:00:51

Existence of a Prime Number Between the Double of Other Primes Conjecture.

Authors: Juan Elias Millas Vera
Comments: 1 Page.

In this paper I show how is possible to do a new application to the Bertrand’s postulate doing a conjecture with 3 prime numbers and the double of 2 of them.
Category: Number Theory

[15] viXra:2011.0199 [pdf] replaced on 2021-03-24 06:29:36

Acknowledgment of Non-linearity or How to Solve Several Conjectures

Authors: Dmitri Martila
Comments: 5 Pages. Submitted to the journal.

Several famous conjectures from Number Theory are studied. I derive a new equivalent formulation of Goldbach's strong conjecture and present an independent conjecture with some evidence for it.
Category: Number Theory

[14] viXra:2011.0198 [pdf] replaced on 2021-03-24 08:56:39

Exceptions from Robin's Inequality

Authors: Dmitri Martila
Comments: 5 Pages. Submitted to the journal.

In this short but rigorous research note I study Robin's Inequality. The number of possible violations of this inequality turns out to be finite. As the finiteness includes zero, I am able to convince you that there are no such violations.
Category: Number Theory

[13] viXra:2011.0191 [pdf] submitted on 2020-11-28 11:00:04

On Fermat's Dividers (Sur Les Diviseurs de Fermat)

Authors: Méhdi Pascal
Comments: 22 Pages.

Fermat's divisors are all integers dividing the polynomial x^n-x, the largest of these divisors is denoted by Z (n) plays an important role in Bernoulli's number theory, it is exactly the denominator of these numbers to one small index shift, for example, whatever the integer x, we have 2730 divided x^13-x, and b(12)=b(13-1)=-691/2730. In this paper we will study some properties of these large Fermat divisors. Résumé : Les diviseurs de Fermat sont tous entiers divisant le polynôme xn-x, le plus grand de ces diviseurs est noté par Z(n) joue un rôle important dans la théorie des nombres de Bernoulli, c’est exactement le dénominateur de ces nombres à un petit décalage d’indice, par exemple, quelque soit l’entier x, on a 2730 divise x^13-x, et b(12)=b(13-1)=-691/2730. Dans ce papier nous allons étudier quelques propriétés de ces grands diviseurs de Fermat.
Category: Number Theory

[12] viXra:2011.0174 [pdf] submitted on 2020-11-24 09:06:32

Fermat's Last Theorem ​as a Consequence of the Little One

Authors: Victor Sorokine
Comments: 2 Pages. [Corrections made by viXra Admin to conform with the requirements on the Submission Form]

In one of Fermat's equivalent equalities, the 3rd digit in the sum of powers a^n+b^n-c^n is not zero and there is a single-valued function of only the last digits a’, b’, c’ ; therefore it cannot be zeroed out with the 2nd and 3rd digits in the sum of bases a+b-c. Apart from the simplest foundations of the theory of a prime number and the consequences of the little theorem, this is, strictly speaking, the proof of the FLT in the first case. See the proof of the second case here: https://vixra.org/pdf/1908.0072v1.pdf .
Category: Number Theory

[11] viXra:2011.0171 [pdf] submitted on 2020-11-24 08:54:38

My Collection of Papers Written to Try to Resolve The abc Conjecture

Authors: Abdelmajid Ben Hadj Salem
Comments: Pages.

In this book, I present my collection of 23 papers written, with different approaches to try to resolve the abc conjecture and others conjectures related to it like c<rad^2(abc). This monograph can give an idea about the advancement of the comprehension of the conjectures related to the problem cited above.
Category: Number Theory

[10] viXra:2011.0143 [pdf] submitted on 2020-11-19 14:01:52

A Solution for Finding Composite Numbers in an Unending Sequence Starting with Prime Numbers

Authors: Eeshan Mundhe
Comments: 5 Pages.

A non-terminating sequence like 31, 331, 3331, 33331, … starts with first seven terms as prime numbers, while the 8th term, which is 333333331, can be expressed as 17 x 19607843. Using Fermat’s Little Theorem, it can be easily proved that there are many more terms in this sequence that are not prime numbers. This paper puts forward a solution to find factors of composite numbers in all such sequences without using Fermat’s Little theorem or divisibility tests. The solution uses a prime number only once to scan all the terms of the unending sequence together, to check if any term is divisible by that prime number instead of checking every term separately, hence reduces the computational complexity. The solution finds the smallest number of the sequence which is divisible by a particular prime number and also proves that it cannot be assumed that all the terms of such sequences will be prime numbers.
Category: Number Theory

[9] viXra:2011.0138 [pdf] replaced on 2024-09-03 20:53:01

Modular Logarithm Unequal

Authors: Sheng-Ping Wu
Comments: 4 Pages.

The main idea of this article is simply calculating integer functions in module. The algebraic in the integer modules is studied in completely new style. By a careful construction, a result is proven that two finite numbers is with unequal logarithms in a corresponding module, and is applied to solving a kind of high degree diophantine equation.
Category: Number Theory

[8] viXra:2011.0113 [pdf] submitted on 2020-11-15 11:49:17

The Euler Product Formula Derived from the Sum of the Power of Primes

Authors: Huang Shan
Comments: 1 Page.

Relate the sum of powers of multiple primes to the sum of powers of natural numbers.
Category: Number Theory

[7] viXra:2011.0112 [pdf] submitted on 2020-11-15 11:49:29

The Solution of Riemann Conjecture and Goldbach Conjecture Derived from the Sum of Prime Numbers

Authors: Huang Shan
Comments: 1 Page.

By connecting the sum of powers of multiple prime numbers with the power sum of natural numbers, the relationship between even numbers in natural numbers and the sum of powers of multiple prime numbers is obtained.
Category: Number Theory

[6] viXra:2011.0080 [pdf] submitted on 2020-11-11 08:44:15

Notation of Zeta Function Using Tangent Number and Research Irrational Number of Special Value of Riemann Zeta Function(N) and L-function(N)

Authors: Takamasa Noguchi
Comments: 7 Pages.

Representation of ζ(2n) using the tangent number and consideration of ζ (2n + 1) and L (2n).
Category: Number Theory

[5] viXra:2011.0057 [pdf] replaced on 2020-11-10 20:00:46

Theory about Rational Prime Numbers

Authors: Juan Elias Millas Vera
Comments: 3 Pages.

Using products of rational numbers and the Eratosthenes method we can find a solution to the problem of rational prime numbers. This kind of numbers is a subset of the rationals and the problem has variations for decimals, centesimals, etc.
Category: Number Theory

[4] viXra:2011.0056 [pdf] submitted on 2020-11-08 20:22:09

On the Proximity of Multiplicative Functions to the Function Omega(n)

Authors: Theophilus Agama
Comments: 5 Pages. submitted to Journal [Corrections made by viXra Admin]

In this paper we examine how closely a multiplicative function resembles an additive function. We show that in fact, given any small $\epsilon>0$, \begin{align}E(\Omega, g;x)\gg \frac{x}{(\log \log x)^{\frac{1}{2}+\epsilon}}\nonumber \end{align} for some choice of multiplicative function, where $\Omega(n)=\sum \limits_{p||n}1$. This is therefore an extension of an earlier result of De Koninck, Doyon and Letendre \cite{de2014proximity}.
Category: Number Theory

[3] viXra:2011.0051 [pdf] submitted on 2020-11-08 11:39:18

Sur Les Formules de Multiplication de Raabe (On Raabe's Multiplication Formulas)

Authors: Méhdi Pascal
Comments: 11 Pages. [Corrections made by viXra Admin to conform with the requirements on the Submission Form]

Determination of the classes of polynomials where we can apply Raabe's Multiplication formulas. Détermination des classes des polynômes où on peut appliquer les formules de Multiplications de Raabe.
Category: Number Theory

[2] viXra:2011.0031 [pdf] replaced on 2021-03-28 21:34:37

An Alternative Method on Sieve of Eratosthenes to Find Prime Numbers

Authors: Olvine Dsouza
Comments: 10 Pages. Only changes has done on title of the research paper.

We introduce ALPHA Prime Theory and ALPHA Prime Series, a new method to find prime numbers and their prime factors (Similar to Sieve of Eratosthenes). We also highlighted the key property that is the additive property of natural numbers which is direct responsible for behavior of prime and composite numbers in natural number line and how it can help us to find prime and composite numbers and its prime factors.
Category: Number Theory

[1] viXra:2011.0003 [pdf] replaced on 2020-11-11 20:05:52

Proof of Goldbach's Conjecture

Authors: Olvin Dsouza
Comments: 15 Pages.

We had taken a unique and a simple approach and tried to prove Goldbach’s conjecture, the famously known conjecture which mathematician throughout the centuries are trying to solve it but always get failed. We know that there are additive property of prime and composite numbers that governs all prime numbers including composites numbers (multiple of two prime numbers) and we have highlighted some of those additive property and proved that Goldbach's conjecture is true.
Category: Number Theory