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Any replacements are listed further down

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

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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

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

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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