Number Theory

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Recent submissions

Any replacements are listed further down

[993] viXra:1508.0295 [pdf] submitted on 2015-08-28 18:54:14

The Endoscopy Over Primes

Authors: Ihsan Raja Muda Nasution
Comments: 1 Page.

In this paper, we analyze the behavior of prime numbers.
Category: Number Theory

[992] viXra:1508.0177 [pdf] submitted on 2015-08-21 06:52:04

Essai Conjecture de Legendre

Authors: MADANI Bouabdallah
Comments: 1 Page. Lier 'Essai Conjecture de Legendre' et 'Résultat Conjecture de Legendre'

Cette note est tirée de mon article 'Essai sur les conjectures de Legendre et de Brocard' non encore publié. Le résultat principal est le Lemme 3. Les calculs sur ce lemme sont donnés dans l'article Résultat Conjecture de Legendre pour n=3,...,1000
Category: Number Theory

[991] viXra:1508.0172 [pdf] submitted on 2015-08-21 12:41:35

Rule About 2

Authors: Jo Hansle
Comments: 1 Page.

I found some rule related to factor 2
Category: Number Theory

[990] viXra:1508.0165 [pdf] submitted on 2015-08-20 11:42:02

Résultats Conjecture de Legendre

Authors: MADANI Bouabdallah
Comments: 18 Pages.

Cette note présente mes résultats sur la conjecture et plus particulièrement le Lemme 3 qui est reconnu comme équivalent à la conjecture. Tableau Primes illustre le lemme 3 pour n=3,...,1000
Category: Number Theory

[989] viXra:1508.0155 [pdf] submitted on 2015-08-19 19:26:41

On The Verification Of Li's Criterion For The Riemann Hypothesis

Authors: Emmanuel Temitope Fondwani
Comments: 5 Pages. Submitted to a formal journal for peer review.

In this paper, we verify a certain criterion of Xian Jin Li whose validity is completely equivalent to the Riemann Hypothesis.
Category: Number Theory

[988] viXra:1508.0150 [pdf] submitted on 2015-08-19 05:59:50

An Elementary Proof of BEAL Conjecture

Authors: Abdelmajid BEN HADJ SALEM
Comments: 21 Pages. The paper was submitted to the journal Integers.

In 1997, Andrew Beal announced the following conjecture : Let A, B,C, m,n, and l be positive integers with m,n,l > 2. If A^m + B^n = C^l then A, B, and C have a common factor. We begin to construct the polynomial P(x)=(x-A^m)(x-B^n)(x+C^l)=x^3-px+q with p,q integers depending of A^m,B^n and C^l. We resolve x^3-px+q=0 and we obtain the three roots x_1,x_2,x_3 as functions of p,q and a parameter µ. Since A^m,B^n,-C^l are the only roots of x^3-px+q=0, we discuss the conditions that x_1,x_2,x_3 are integers.
Category: Number Theory

[987] viXra:1508.0137 [pdf] submitted on 2015-08-17 07:42:55

The Law of Filling Out that Proves Goldbach(1+1)&(P+2)

Authors: Aaron Chau
Comments: 6 Pages. Attached with Chinese language for reference

The concept of the first numbers with the interval between 2 has existed in east for more than 3,000 years, even though the oriental mathematicians are not familiar with this concept. After 14 years research, I have found the law of filling out could prove(1+1)&(P+2). This article explained very clearly about this law, and it is very helpful to solve the Goldbach Conjecture.
Category: Number Theory

[986] viXra:1508.0122 [pdf] submitted on 2015-08-16 05:43:45

Affirmative Resolve of Riemann Hypothesis

Authors: T.Nakashima
Comments: 5 Pages.

This paper is the rewrite of "The anzwer of the axiom that equivarent to Riemann Hypothesis".
Category: Number Theory

[985] viXra:1508.0109 [pdf] submitted on 2015-08-14 11:09:04

X^p-Y^p=a^p B^p ?

Authors: Maik Becker-Sievert
Comments: 1 Page.

X^p-Y^p=A^p B^p Has no number solutions in N ; p = odd primes
Category: Number Theory

[984] viXra:1508.0069 [pdf] submitted on 2015-08-10 05:05:03

A³+B³=C³ ?

Authors: Maik Becker-Sievert
Comments: 1 Page.

A short proof of Eulers Cubus Theorem
Category: Number Theory

[983] viXra:1508.0034 [pdf] submitted on 2015-08-04 10:44:46

A New Conjecture in Number Theory

Authors: Dao Thanh Oai
Comments: 1 Page.

I propose a new conjecture of generalization of the Fermat last theorem and the Lander, Parkin, and Selfridge conjecture.
Category: Number Theory

[982] 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

[981] 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

[980] 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

[979] 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

[978] 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

[977] 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

[976] 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

[975] 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

[974] 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

[973] 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

[972] 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

[971] 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

[970] 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

[969] 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

[968] 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

[967] 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

[966] 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

[965] 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

[964] 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

Replacements of recent Submissions

[467] viXra:1508.0165 [pdf] replaced on 2015-08-20 22:26:38

Résultat Conjecture de Legendre.

Authors: M. MADANI Bouabdallah
Comments: 18 Pages.

Cette note présente mes résultats (Lemme 3)sur la conjecture de Legendre. Le lemme 3 a été reconnu comme équivalent à la conjecture de Legendre. Tableau Primes illustre le Lemme 3 pour n=3,...,1000
Category: Number Theory

[466] viXra:1508.0150 [pdf] replaced on 2015-08-19 08:00:38

An Elementary Proof of BEAL Conjecture

Authors: Abdelmajid BEN HADJ SALEM
Comments: 21 Pages.

In 1997, Andrew Beal announced the following conjecture : Let A, B,C, m,n, and l be positive integers with m,n,l > 2. If A^m + B^n = C^l then A, B, and C have a common factor. We begin to construct the polynomial P(x)=(x-A^m)(x-B^n)(x+C^l)=x^3-px+q with p,q integers depending of A^m,B^n and C^l. We resolve x^3-px+q=0 and we obtain the three roots x_1,x_2,x_3 as functions of p,q and a parameter µ. Since A^m,B^n,-C^l are the only roots of x^3-px+q=0, we discuss the conditions that x_1,x_2,x_3 are integers.
Category: Number Theory

[465] viXra:1508.0137 [pdf] replaced on 2015-08-24 07:16:41

The Law of Filling Out that Proves Goldbach(1+1)&(P+2)

Authors: Aaron Chau
Comments: 6 Pages. Attached with Chinese language for reference

The concept of the first numbers with the interval between 2 has existed in east for more than 3,000 years, even though the oriental mathematicians are not familiar with this concept. After 14 years research, I have found the law of filling out could prove(1+1)&(P+2). This article explained very clearly about this law, and it is very helpful to solve the Goldbach Conjecture.
Category: Number Theory

[464] viXra:1508.0122 [pdf] replaced on 2015-08-29 09:20:48

Affirmative Resolve of Riemann Hypothesis

Authors: T.Nakashima
Comments: 5 Pages.

This paper is the rewrite of "The anzwer of the axiom that equivarent to Riemann Hypothesis".
Category: Number Theory

[463] viXra:1508.0122 [pdf] replaced on 2015-08-21 08:57:26

Affirmative Resolve of Riemann Hypothesis

Authors: T.Nakashima
Comments: 5 Pages.

This paper is the rewrite of "The anzwer of the axiom that equivarent to Riemann Hypothesis".
Category: Number Theory

[462] viXra:1508.0034 [pdf] replaced on 2015-08-08 06:37:35

A New Conjecture in Number Theory

Authors: Dao Thanh Oai
Comments: 1 Page.

I propose a conjecture of generalization of the Fermat last theorem and the Lander, Parkin, and Selfridge conjecture.
Category: Number Theory

[461] viXra:1508.0034 [pdf] replaced on 2015-08-06 21:07:38

A New Conjecture in Number Theory

Authors: Dao Thanh Oai
Comments: 1 Page.

I propose a new conjecture of generalization of the Fermat last theorem and the Lander, Parkin, and Selfridge conjecture.
Category: Number Theory

[460] viXra:1508.0005 [pdf] replaced on 2015-08-08 06:41:42

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

[459] 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

[458] 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

[457] 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

[456] viXra:1507.0196 [pdf] replaced on 2015-08-05 12:32:55

Conjecture de C.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 nombres premiers ,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

[455] 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

[454] 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

[453] 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

[452] 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

[451] 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