Number Theory

1508 Submissions

[14] viXra:1508.0430 [pdf] submitted on 2015-08-31 20:38:15

How Many Primes in 100 Consecutive Integers?

Authors: Marco Ripà, Gabriele Tessaro, Andrea Forti
Comments: 4 Pages.

In this paper we study for which m ∈ N_0 there is a finite number of distinct k ∈ ℕ-{0} such that [k, k+99] contains m primes. On the contrary, we prove that the distinct values of k are not finite if m≤1, while there is no k for any m>26. In conclusion, we will discuss the current state of research in this field, advancing also a few speculations as regards to the above-mentioned subject.
Category: Number Theory

[13] viXra:1508.0426 [pdf] submitted on 2015-08-31 09:22:58

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

Authors: Diego Liberati
Comments: 1 Page.

A proof of the conjecture in the title is offered
Category: Number Theory

[12] viXra:1508.0295 [pdf] replaced on 2015-12-09 20:25:38

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

[11] 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

[10] 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

[9] 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

[8] viXra:1508.0150 [pdf] replaced on 2015-10-02 05:24:46

Une Démonstration Elémentaire de la Conjecture de BEAL

Authors: Abdelmajid Ben Hadj Salem
Comments: 31 Pages. New version, in French.

En 1997, Andrew Beal \cite{B1} avait annoncé la conjecture suivante: \textit{Soient $A, B,C, m,n$, et $l$ des entiers positifs avec $m,n,l > 2$. Si $A^ m + B^n = C^l$ alors $A, B,$ et $C$ ont un facteur commun.} Nous commençons par construire le polynôme $P(x)=(x-A^m)(x-B^n)(x+C^l)=x^3-px+q$ avec $p,q$ des entiers qui dépendent de $A^m,B^n$ et $C^l$. Nous résolvons $x^3-px+q=0$ et nous obtenons les trois racines $x_1,x_2,x_3$ comme fonctions de $p,q$ et d'un paramètre $\theta$. Comme $A^m,B^n,-C^l$ sont les seules racines de $x^3-px+q=0$, nous discutons les conditions pourque $x_1,x_2,x_3$ soient des entiers. Des exemples numériques sont présentés.
Category: Number Theory

[7] 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

[6] viXra:1508.0122 [pdf] replaced on 2016-08-14 03:41:08

Affirmative Resolve of Riemann Hypothesis

Authors: T.Nakashima
Comments: 6 Pages.

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

[5] 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

[4] 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

[3] 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

[2] 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

[1] 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