Number Theory

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Recent submissions

Any replacements are listed further down

[987] viXra:1508.0025 [pdf] submitted on 2015-08-03 01:53:31

The Symbiosis Ambiguity of Binomial Theorem and Some Types of Countable Sets.

Authors: Reuven Tint, Michael Tint
Comments: 10 Pages. Original article is written in Russian.

We show ("transparently") that by using a new binomial expansion identically equal to the classical, received ambiguous numerical sequences (countable sets) of arbitrary length, smaller infinity, in which the coefficients of each degree "x" can be either identical zero and not equal to zero simultaneously.
Category: Number Theory

[986] viXra:1508.0008 [pdf] submitted on 2015-08-01 07:11:03

There Are Infinitely Many Primes of the Form N^2+1

Authors: Diego Liberati
Comments: 1 Page.

A proof of the conjecture is offered
Category: Number Theory

[985] viXra:1508.0005 [pdf] submitted on 2015-08-01 01:58:45

Two Conjectures in Number Theory

Authors: Dao Thanh Oai
Comments: 1 Page.

In this note, I propose a conjecture of generalization of the Fermat Last Theorem and a conjecture of generalization of the Beal's conjecture.
Category: Number Theory

[984] viXra:1507.0202 [pdf] submitted on 2015-07-27 17:35:22

The Significance Of The Non-Trivial Zeros Of The Riemann Zeta Function

Authors: Bertrand Wong
Comments: 3 Pages.

This paper expounds the role of the non-trivial zeros of the Riemann zeta function ζ and supplements the author’s earlier papers on the Riemann hypothesis. There is a lot of mystery surrounding the non-trivial zeros.
Category: Number Theory

[983] viXra:1507.0200 [pdf] submitted on 2015-07-27 14:05:43

Conjecture de Collatz (Syracuse) Démonstration

Authors: BERKOUK Mohamed
Comments: 10 Pages.

la démonstration passe par trois étapes : 1° - l’unicité du cycle trivial 2° - la décroissance de tout N du départ 3° - l’atterrissage systématique vers le cycle trivial . la démonstration de ces trois étape implique la démonstration de la conjecture de Collatz.
Category: Number Theory

[982] viXra:1507.0197 [pdf] submitted on 2015-07-27 05:09:58

A Proof of the Goldbach Conjecture

Authors: Diego Liberati
Comments: Pages.

The so called strong form is shown to derive from the recently proved so called weak form
Category: Number Theory

[981] viXra:1507.0196 [pdf] submitted on 2015-07-26 18:47:31

Conjecture de C.goldbach Démons.

Authors: BERKOUK Mohamed
Comments: 9 Pages.

Ceci est une démonstration de la conjecture du C.GOLDBACH aussi bien la forte que la faible dans sa version moderne , qui repose sur le théorème de WARING ,puis sur un théorème sur les NP que j'avais développé pour conclure sur la primalité (v.multimorielle), enfin un 3° théorème qui annonce la propriété de la parité de la somme et le produit de tout entier naturel .
Category: Number Theory

[980] viXra:1507.0188 [pdf] submitted on 2015-07-25 05:10:50

The Levy_ Bertrand_ Goldbach Proof

Authors: Maik Becker-Sievert
Comments: 1 Page.

Proofed Bertrands Postulate Goldbach´s Ternär and Binär Conjecture Levy´s Conjecture
Category: Number Theory

[979] viXra:1507.0176 [pdf] submitted on 2015-07-23 10:38:51

Real Multiplication Nature and Its Scaling Factors

Authors: Andrea Pignataro
Comments: 7 Pages.

The goal of this paper is to explain that the real nature of the multiplication operation is based on its scaling factors and why is a common mistake to understand the multiplication as a repeated addition.
Category: Number Theory

[978] viXra:1507.0171 [pdf] submitted on 2015-07-22 10:30:11

An Elementary Proof Of Fermat,s Last Theorem

Authors: Bezaliel Anotida Joshua
Comments: 5 Pages.

In this paper, we provide an elementary proof of Fermat,s Las Theorem
Category: Number Theory

[977] viXra:1507.0150 [pdf] submitted on 2015-07-20 04:45:42

A Partial Proof of Carmichael Conjecture

Authors: Neelah Deka
Comments: 4 Pages.

In this note,we shall give a partial proof of carmichael conjecture
Category: Number Theory

[976] viXra:1507.0140 [pdf] submitted on 2015-07-18 04:51:43

On the Existence of at Least One Prime Number Between 5n and 6n.

Authors: Irsen Virnoy
Comments: 3 Pages.

One of the still unsolved conjectures related to prime numbers states that for all integers n>k>1 there exists at least one prime number in the interval [kn; (k+1)n]. The case k = 1 is called Bertrand's postulate, which was proved Chebyshev in the year 1850. M. El Bachraoui proved the case k = 2 in 2006, and the case k = 2 was proved by Andy Loo in 2011. This paper gives the proof for the case when k = 5.
Category: Number Theory

[975] viXra:1507.0100 [pdf] submitted on 2015-07-14 12:28:24

Disproof the Four Counterexamples for Beal's Conjecture

Authors: Valdir Monteiro dos Santos Godoi
Comments: 1 Page.

Probably by mistake, was published a paper which intended give some counterexamples of the Beal’s conjecture. The four examples in that paper are wrong.
Category: Number Theory

[974] viXra:1507.0091 [pdf] submitted on 2015-07-14 03:19:52

A New Conjecture on Prime Numbers

Authors: Neelabh Deka
Comments: 1 Page. A new conjecture on prime numbers is proposed in this short note.

A new conjecture on prime numbers is proposed in this short note.
Category: Number Theory

[973] viXra:1507.0033 [pdf] submitted on 2015-07-05 12:35:58

(pk mk qk) or an Unexpected Simplicity

Authors: Ralf Wüsthofen
Comments: 1 Page. full version under 1403.0083

This note is a summary of a detailed proof ² of the strong Goldbach conjecture. We show that the conjecture can be immediately derived from an appropriate structuring of the natural numbers. As an additional result of this structuring we can even obtain a strengthened form of the conjecture.
Category: Number Theory

[972] viXra:1507.0021 [pdf] submitted on 2015-07-03 07:04:05

La Conjecture de Polignac-Démo.docx

Authors: BERKOUK mohamed
Comments: 1 Page.

démonstration résumée , sans détailler les théorèmes de WARING ,EUCLIDE et le théorème des nombres premiers (TNP) que j'ai utilisé pour asseoir les jalons d'une démonstration de La conjecture de POLIGNAC.
Category: Number Theory

[971] viXra:1507.0013 [pdf] submitted on 2015-07-02 04:54:16

A Note About Power Function(Part 2)

Authors: Kolosov Petya
Comments: 11 Pages. -

In this paper described some new view and properties of the power function, the main aim of the work is to enter some new ideas. Also described expansion of power function, based on done research. Expansion has like Binominal theorem view, but algorithm not same.
Category: Number Theory

[970] viXra:1507.0004 [pdf] submitted on 2015-07-01 00:45:24

An Elementary Proof of the Riemann Hypothesis

Authors: Diego Liberati
Comments: 1 Page.

An elementary proof of the Riemann hypothesis is offered
Category: Number Theory

[969] viXra:1507.0001 [pdf] submitted on 2015-07-01 00:30:41

An Elementary Proof of the Twin Primes Conjecture

Authors: Diego Liberati
Comments: 1 Page.

An elementary proof to the twin prime conjecture is offered
Category: Number Theory

[968] viXra:1506.0198 [pdf] submitted on 2015-06-27 13:35:52

The Algorithm for Recurrent Finding Countless Coprime Integer Solutions of Diophantine Equations

Authors: Reuven Tint, Michael Tint
Comments: 34 Pages. Original article is written in Russian.

In the history of mathematics attempts to find common solutions in integers of Diophantine equations were unsuccessful (except iterate through numbers).In this paper, we obtain an algorithm (identity) of recurrent finding countless coprime integer solutions to equations x^4+y^4=a^4+b^4 , x^4=y^4+a^4+b^4 and some arising from these extraordinary consequences.
Category: Number Theory

[967] viXra:1506.0190 [pdf] submitted on 2015-06-26 19:21:21

General Divisibility’s Criteria

Authors: Mouhcine AMRAR / BACCALAUREAT SCIENCES MATHEMATIQUES
Comments: 4 Pages.

This work is a study of divisibility and these criteria, in which we will give general relationships and divisibility criteria. We begin this work by answering the following question: what conditions should check the digits dialing the number to make it divisible by d? Among the most known and used criteria are the divisibility by 2, 3, 5, 11...
Category: Number Theory

[966] viXra:1506.0189 [pdf] submitted on 2015-06-26 19:25:11

All About Prime Numbers

Authors: Mouhcine AMRAR
Comments: 4 Pages.

WE GIVE ALL ABOUT PRIME NUMBERS
Category: Number Theory

[965] viXra:1506.0145 [pdf] submitted on 2015-06-18 15:52:27

The Solution of Some Transcendence Conjectures Over Field Q by Using Algebra of Dedekind Hyperreals

Authors: Jaykov Foukzon
Comments: 48 Pages.

In this paper the important applications of the Dedekind completion *R_d in transcendental number theory is considered. Given any analytic function of one complex variable f ∈Q[z_1,z_2, . . .],we investigate the arithmetic nature of the values of f(z) at transcendental points e^n. Main results are: (i) the both numbers e+pi and e-pi are irrational, (ii) number e^e are transcendental.
Category: Number Theory

[964] viXra:1506.0144 [pdf] submitted on 2015-06-18 19:58:00

The Distribution of Prime Number in a Interval

Authors: Yu Zhang
Comments: 6 Pages.

The Goldbach theorem and the twin prime theorem are homologous.the paper from the prime origin,derived the equations of the twin prime theorem and the Goldbach theorem,and new prime number theorem.
Category: Number Theory

[963] viXra:1506.0142 [pdf] submitted on 2015-06-18 14:55:33

The Non-Trivial Zeros Of The Riemann Zeta Function

Authors: Bertrand Wong
Comments: 9 Pages.

This paper shows why the non-trivial zeros of the Riemann zeta function ζ must always be on the critical line Re(s) = 1/2 and not anywhere else on the critical strip bounded by Re(s) = 0 and Re(s) = 1, thus affirming the validity of the Riemann hypothesis.
Category: Number Theory

[962] viXra:1506.0121 [pdf] submitted on 2015-06-15 15:35:17

The Conjoncture of Goldbach

Authors: Jean Pierre Morvan
Comments: 16 Pages.

My first proposal for a demonstration goes back to 1997, well before the editions Faber and Faber allot a bonus of 1 million dollars to that which would show the conjecture of Goldbach. Since this date, i proposed different versions on the form,but unchanged on the bottom. In 1742, the conjecture of Goldbach was “All even number ; writing as the sum of prime numbers”. The number 1 was regarded as a prime number.
Category: Number Theory

[961] viXra:1506.0102 [pdf] submitted on 2015-06-13 11:08:31

Study on the Goldbach Conjecture

Authors: Guacho Perez
Comments: 3 Pages.

A simple study on the Goldbach Conjecture and its links to the Prime Number Theorem and Bertrand's Postulate.
Category: Number Theory

[960] viXra:1506.0082 [pdf] submitted on 2015-06-11 05:02:31

Strong Filtration on the Critical Line

Authors: Ihsan Raja Muda Nasution
Comments: 1 Page.

In this paper, we delete the zeros of the critical line.
Category: Number Theory

[959] viXra:1506.0066 [pdf] submitted on 2015-06-08 07:01:07

A Concise Proof of Fermat's Last Theorem

Authors: J. Yun
Comments: 1 page

This paper offers a concise proof of Fermat’s Last Theorem using the Euclidean algorithm.
Category: Number Theory

[958] viXra:1506.0065 [pdf] submitted on 2015-06-08 07:37:03

Perfect Cuboid is not Possible

Authors: V.I. Saenko
Comments: 7 Pages.

A perfect cuboid, i.e., a rectangular parallelepiped having integer edges, integer face diagonals, and integer space diagonal, is proved to be is not possible.
Category: Number Theory

[957] viXra:1506.0048 [pdf] submitted on 2015-06-06 05:02:36

A Concise Proof of Beal’s Conjecture

Authors: J. Yun
Comments: 1 Page.

This paper offers a concise proof of Beal’s conjecture using the identity.
Category: Number Theory

[956] viXra:1506.0047 [pdf] submitted on 2015-06-06 05:04:27

A Plain Proof of Fermat’s Last Theorem

Authors: J. Yun
Comments: 1 Page.

This paper offers a plain proof of Fermat’s Last Theorem using the cosine rule.
Category: Number Theory

[955] viXra:1506.0046 [pdf] submitted on 2015-06-06 05:11:43

A Plain Proof of Beal’s Conjecture

Authors: J. Yun
Comments: 1 Page.

This paper offers a plain proof of Beal’s conjecture using the cosine rule.
Category: Number Theory

[954] viXra:1506.0041 [pdf] submitted on 2015-06-05 13:47:14

Anti Aristotle - The Division Of Zero By Zero

Authors: Jan Pavo Barukčić, Ilija Barukčić
Comments: 12 pages. (C)Jan Pavo Barukčić,Department of Mathematics and Computer Sciences, University of Münster, Einsteinstr. 62, 48149 Münster, Germany and Ilija Barukčić, Jever, Germany, 2014,

Today, the division of zero by zero (0/0) is a concept in philosophy, mathematics and physics without a definite solution. On this view, we are left with an inadequate and unsatisfactory situation that we are not allowed to divide zero by zero while the need to divide zero by zero (i. e. divide a tensor component which is equal to zero by another tensor component which is equal to zero) is great. A solution of the philosophically, logically, mathematically and physically far reaching problem of the division of zero by zero (0/0) is still not in sight. The aim of this contribution is to solve the problem of the division of zero by zero (0/0) while relying on Einstein's theory of special relativity. In last consequence, Einstein's theory of special relativity demands the division of zero by zero. Due to Einstein's theory of special relativity it is (0/0) = 1. As we will see, either we must accept the division of zero by zero as possible and defined or we must abandon Einstein's theory of special relativity as refuted.
Category: Number Theory

[953] viXra:1505.0228 [pdf] submitted on 2015-05-30 10:27:21

Real Numbers

Authors: C. A. Laforet
Comments: 13 Pages.

In this paper, a geometric interpretation of the expression Z_1 〖[Z_0]〗^(Z_2 ), where Z_0, Z_1, and Z_2 are complex numbers is investigated. The term real number in the context of this paper is defined as any number Z=ri^θ where r and θ are rational quantities and i^θ=e^(π/2 iθ) (the angular unit in which θ is measured is defined as the iota). It is proposed that multiplication of Z_0 by Z_1 and exponentiation of Z_0 by Z_2 do not modify the number itself but rather modify the basis in which the number is represented relative to what is referred to as the Rest Basis, which is the well-known rectangular complex plane. Equations that are functions of the magnitudes and angles of Z_0, Z_1, and Z_2 are derived that quantify the basis transformations in the general case. Finally, it is proposed that real numbers as well as the bases in which the numbers are represented can be understood as pairs of helical structures with one helix representing the angular component of the number and the other helix representing the magnitude of the number. It is shown that exponentiation by a complex number can be view as interactions between these two helices.
Category: Number Theory

[952] viXra:1505.0205 [pdf] submitted on 2015-05-27 08:21:06

The Null Ortho-Linearity

Authors: Ihsan Raja Muda Nasution
Comments: 2 Pages.

We diagnose the body of the critical strip. Thereby, we can extract the deterministic location of the critical line.
Category: Number Theory

[951] viXra:1505.0203 [pdf] submitted on 2015-05-26 15:26:42

A Prospect Proof of the Goldbach's Conjecture

Authors: Douadi MIHOUBI
Comments: 19 Pages.

Based on, the well-ordering (N,<) of the set of natural numbers N, and some basic concepts of number theory, and using the proof by contradiction and the inductive proof on N, we prove that the validity of the Goldbach's statement: every even integer 2n > 4, with n > 2, is the sum of two primes. This result confirms the Goldbach conjecture, which allows to inserting it as theorem in number theory. Key Words: Well-ordering (N,<), basic concepts and theorems on number theory, the indirect and inductive proofs on natural numbers. AMS 2010: 11AXX, 11p32, 11B37.
Category: Number Theory

Replacements of recent Submissions

[455] viXra:1508.0005 [pdf] replaced on 2015-08-03 05:23:19

Two Conjectures in Number Theory

Authors: Dao Thanh Oai
Comments: 1 Page.

In this note, I propose a conjecture of generalization of the Lander, Parkin, and Selfridge conjecture; and a conjecture of generalization of the Beal's conjecture.
Category: Number Theory

[454] viXra:1508.0005 [pdf] replaced on 2015-08-02 21:31:55

Two Conjectures in Number Theory

Authors: Dao Thanh Oai
Comments: 1 Page.

In this note, I propose a conjecture of generalization of the Lander, Parkin, and Selfridge conjecture; and a conjecture of generalization of the Beal's conjecture.
Category: Number Theory

[453] viXra:1507.0202 [pdf] replaced on 2015-07-29 13:06:11

The Significance Of The Non-Trivial Zeros Of The Riemann Zeta Function

Authors: Bertrand Wong
Comments: 3 Pages.

This paper expounds the role of the non-trivial zeros of the Riemann zeta function ζ and supplements the author’s earlier papers on the Riemann hypothesis. There is a lot of mystery surrounding the non-trivial zeros.
Category: Number Theory

[452] viXra:1507.0196 [pdf] replaced on 2015-07-27 15:40:14

Conjecture de Christian Goldbach Demonstration

Authors: BERKOUK Mohamed
Comments: 9 Pages.

Ceci est une démonstration de la conjecture du C.GOLDBACH aussi bien la forte que la faible dans sa version moderne , qui repose sur le théorème de WARING ,puis sur un théorème sur les NP que j'avais développé pour conclure sur la primalité (v.multimorielle), enfin un 3° théorème qui annonce la propriété de la parité de la somme et le produit de tout entier naturel .
Category: Number Theory

[451] viXra:1507.0171 [pdf] replaced on 2015-07-24 07:22:01

An Elementary Proof Of Fermat's Last Theorem

Authors: Bezaliel Anotida Joshua
Comments: 5 Pages. Submitted to a formal journal for peer-review.

In this note, we provide an elementary proof of Fermat's Last Theorem.
Category: Number Theory

[450] viXra:1507.0004 [pdf] replaced on 2015-07-02 09:36:07

A Proof of the Riemann Hypothesis

Authors: Diego Liberati
Comments: Pages.

Taking into account infinitesimal and iperreal concepts from Robinsons' non standard analysis the proof in the previous versions has been made more general
Category: Number Theory

[449] viXra:1507.0004 [pdf] replaced on 2015-07-02 00:59:47

A Revised Elementary Proof of the Riemann Hypothesis

Authors: Diego Liberati
Comments: 1 Page.

A revised version of the elementary proof proposed yesterday: now positive integers are correctly called naturals
Category: Number Theory

[448] viXra:1507.0001 [pdf] replaced on 2015-07-14 00:34:22

A Proof of the Twin Primes Conjecture

Authors: Diego Liberati
Comments: Pages.

An elementary proof to the twin prime conjecture is offered
Category: Number Theory

[447] viXra:1506.0145 [pdf] replaced on 2015-07-19 07:43:00

The Solution of Some Very Old Transcendence Conjectures Over Field Q by Using Algebra of Dedekind Hyperreals

Authors: Jaykov Foukzon
Comments: 54 Pages.

In this paper the important applications of the Dedekind completion *R_d in transcendental number theory is considered. Given any analytic function of one complex variable f ∈Q[[z]],we investigate the arithmetic nature of the values of f(z) at transcendental points e^n. Main results are: (i) the both numbers e+pi and e-pi are irrational, (ii) number e^e are transcendental. Nontrivial generalization of the Lindemann-Weierstrass theorem is obtained.
Category: Number Theory

[446] viXra:1506.0144 [pdf] replaced on 2015-07-03 09:36:48

The Distribution of Prime Number in a Interval

Authors: Yu Zhang
Comments: 6 Pages.

The Goldbach theorem and the twin prime theorem are homologous.the paper from the prime origin,derived the equations of the twin prime theorem and the Goldbach theorem,and new prime number theorem.
Category: Number Theory

[445] viXra:1506.0142 [pdf] replaced on 2015-06-22 11:08:28

The Non-Trivial Zeros Of The Riemann Zeta Function

Authors: Bertrand Wong
Comments: 9 Pages.

This paper shows why the non-trivial zeros of the Riemann zeta function ζ will always be on the critical line Re(s) = 1/2 and not anywhere else on the critical strip bounded by Re(s) = 0 and Re(s) = 1, thus affirming the validity of the Riemann hypothesis.
Category: Number Theory

[444] viXra:1506.0142 [pdf] replaced on 2015-06-22 01:01:38

The Non-Trivial Zeros Of The Riemann Zeta Function

Authors: Bertrand Wong
Comments: 9 Pages.

This paper shows why the non-trivial zeros of the Riemann zeta function ζ must always be on the critical line Re(s) = 1/2 and not anywhere else on the critical strip bounded by Re(s) = 0 and Re(s) = 1, thus affirming the validity of the Riemann hypothesis.
Category: Number Theory

[443] viXra:1506.0142 [pdf] replaced on 2015-06-20 06:44:32

The Non-Trivial Zeros Of The Riemann Zeta Function

Authors: Bertrand Wong
Comments: 9 Pages.

This paper shows why the non-trivial zeros of the Riemann zeta function ζ must always be on the critical line Re(s) = 1/2 and not anywhere else on the critical strip bounded by Re(s) = 0 and Re(s) = 1, thus affirming the validity of the Riemann hypothesis.
Category: Number Theory

[442] viXra:1505.0205 [pdf] replaced on 2015-06-01 04:09:41

The Null Ortho-Linearity

Authors: Ihsan Raja Muda Nasution
Comments: 2 Pages.

We diagnose the body of the critical strip. Thereby, we can extract the deterministic location of the critical line.
Category: Number Theory