Number Theory

1803 Submissions

[20] viXra:1803.0715 [pdf] submitted on 2018-03-30 04:02:45

Queens Puzzle

Authors: Andrey B. Skrypnik
Comments: 13 Pages.

Complete solution of Queens Puzzle
Category: Number Theory

[19] viXra:1803.0689 [pdf] submitted on 2018-03-28 06:44:40

Le Monde Des Nombres Premiers

Authors: BERKOUK Mohamed
Comments: 27 Pages.

et si nous essayons d'extraire les nombres composés de l'ensemble des entiers naturels , à commencer par trouver la formule qui génère tous les entiers sans les multiple de 2 et 3 ( 1er polynôme ) puis de générer les entiers sans les multiples de 2,3,5 (2eme polynôme ) le but est de trouver l’équation , la formule ou le polynôme qui ne génèrera que les NOMBRES PREMIERS...
Category: Number Theory

[18] viXra:1803.0668 [pdf] replaced on 2018-04-18 10:58:01

On The Proving Method of Fermat's Last Theorem

Authors: Haofeng Zhang
Comments: 19 Pages.

In this paper the author gives an elementary mathematics method to solve Fermat's Last Theorem (FLT), in which let this equation become an one unknown number equation, in order to solve this equation the author invented a method called “Order reducing method for equations”, where the second order root compares to one order root, and with some necessary techniques the author successfully proved when x^(n-1)+y^(n-1)- z^(n-1) <= x^(n-2)+y^(n-2)-z^(n-2) there are no positive solutions for this equation, and also proves with the increasing of x there are still no positive integer solutions for this equation when x^(n-1)+y^(n-1)- z^(n-1)<=x^(n-2)+y^(n-2)- z^(n-2) is not satisfied.
Category: Number Theory

[17] viXra:1803.0654 [pdf] submitted on 2018-03-25 19:15:54

Sum of Simple Composite Numbers by Golden Patterns

Authors: Zeolla Gabriel Martín
Comments: 5 Pages.

This paper develops the formula that calculates the sum of simple composite numbers by golden patterns.
Category: Number Theory

[16] viXra:1803.0635 [pdf] submitted on 2018-03-23 20:55:27

A Note on Properties of a Prime-Generating Quadratic 13n^2 + 53n + 41

Authors: Waldemar Puszkarz
Comments: 2 Pages.

This note presents some properties of a quadratic polynomial 13n^2 + 53n + 41. One of them is unique, while others are shared with other prime-generating quadratics. The main purpose of this note is to emphasize certain common features of such quadratics that may not have been noted before.
Category: Number Theory

[15] viXra:1803.0546 [pdf] submitted on 2018-03-23 10:15:03

A Note on Some Class of Prime-Generating Quadratics

Authors: Waldemar Puszkarz
Comments: 3 Pages.

This note lists all the known prime-generating quadratics with at most two-digit positive coefficients that generate at least 20 primes in a row. The Euler polynomial is the best-known member of this class of six.
Category: Number Theory

[14] viXra:1803.0493 [pdf] submitted on 2018-03-22 22:28:25

Prime Number Prediction Formula

Authors: Elizabeth Gatton-Robey
Comments: 22 Pages.

The current mathematical consensus is that Prime numbers, those integers only divisible by one and themselves, follow no standard predictable pattern. This body of work provides the first formula to predict prime numbers. In doing so, this proves that prime numbers follow a pattern, and proves Goldbach’s Conjecture to be true. This is done by forming an algorithm that considers all even integers, systematically eliminates some, and the resulting subset of even integers produces all prime numbers once three is subtracted from each.
Category: Number Theory

[13] viXra:1803.0362 [pdf] submitted on 2018-03-21 07:57:40

Question 444 : Tribonacci Constant and Pi

Authors: Edgar Valdebenito
Comments: 3 Pages.

This note presents some formulas related with pi.
Category: Number Theory

[12] viXra:1803.0317 [pdf] replaced on 2018-04-09 06:07:22

Analysis of Riemann's Hypothesis

Authors: John Atwell Moody
Comments: 8 Pages.

Let p(c,r,v)=e^{(c-1)(r+2v)} log({{\lambda(r+v)}\over{q(r+v)}}) log({{\lambda(v)}\over{q(v)}}), f(c,r)=\int_{-\infty}^\infty p(c,r,v)+p(c,-r,v) dv. Let c be a real number such that 0 Suppose that

f(c,r)<0 and {{\partial}\over{\partial r}}f(c,r)>0 for all $r\ge 0$ while {{\partial}\over{\partial c}}f(c,r)<0 and {{\partial^2}\over {\partial c \partial r}}f(c,r)>0 for all r>0.

Then \zeta(c+i\omega) \ne 0 for all \omega.
Category: Number Theory

[11] viXra:1803.0298 [pdf] submitted on 2018-03-20 21:42:49

Simple Composite Numbers by Golden Patterns

Authors: Zeolla Gabriel Martin
Comments: 3 Pages.

This paper develops the formula that calculates the quantity of simple composite numbers that exist by golden patterns.
Category: Number Theory

[10] viXra:1803.0289 [pdf] submitted on 2018-03-21 03:18:10

New Discovery on Goldbach Conjecture

Authors: Bado idriss olivier
Comments: 6 Pages.

In this paper we are going to give the proof of Goldbach conjecture by introducing a new lemma which implies Goldbach conjecture .By using Chebotarev-Artin theorem , Mertens formula and Poincare sieve we establish the lemma
Category: Number Theory

[9] viXra:1803.0225 [pdf] submitted on 2018-03-15 20:17:04

Sum of Simple Prime Numbers

Authors: Zeolla Gabriel martin
Comments: 4 Pages.

This paper develops the formula that calculates the sum of simple prime numbers by golden pattern.
Category: Number Theory

[8] viXra:1803.0219 [pdf] submitted on 2018-03-16 05:37:57

Redefining Imaginary and Complex Numbers, Defining Imaginary and Complex Objects

Authors: Huseyin Ozel
Comments: 44 Pages.

The existing definition of imaginary numbers is solely based on the fact that certain mathematical operation, square operation, would not yield certain type of outcome, negative numbers; hence such operational outcome could only be imagined to exist. Although complex numbers actually form the largest set of numbers, it appears that almost no thought has been given until now into the full extent of all possible types of imaginary numbers. A close look into what further non-existing numbers could be imagined help reveal that we could actually expand the set of imaginary numbers, redefine complex numbers, as well as define imaginary and complex mathematical objects other than merely numbers.
Category: Number Theory

[7] viXra:1803.0179 [pdf] submitted on 2018-03-12 18:18:40

Continuity, Non-Constant Rate of Ascent, & The Beal Conjecture

Authors: Morgan Osborne
Comments: 22 Pages. Keywords: Beal, Diophantine, Continuity (2010 MSC: 11D99, 11D41)

The Beal Conjecture considers positive integers A, B, and C having respective positive integer exponents X, Y, and Z all greater than 2, where bases A, B, and C must have a common prime factor. Taking the general form A^X + B^Y = C^Z, we explore a small opening in the conjecture through reformulation and substitution to create two new variables. One we call 'C dot' representing and replacing C and the other we call 'Z dot' representing and replacing Z. With this, we show that 'C dot' and 'Z dot' are separate continuous functions, with argument (A^X + B^Y), that achieve all positive integers during their continuous non-constant rates of infinite ascent. Possibilities for each base and exponent in the reformulated general equation A^X +B^Y = ('C dot')^('Z dot') are examined using a binary table along with analyzing user input restrictions and 'C dot' values relative to A and B. Lastly, an indirect proof is made, where conclusively we find the continuity theorem to hold over the conjecture.
Category: Number Theory

[6] viXra:1803.0178 [pdf] replaced on 2018-03-16 15:50:40

Simple Prime Numbers Per Golden Patterns

Authors: Zeolla Gabriel Martin
Comments: 3 Pages.

This paper develops the formula that calculates the quantity of simple prime numbers that exist by golden patterns.
Category: Number Theory

[5] viXra:1803.0121 [pdf] submitted on 2018-03-09 10:43:27

Construction of the Golden Patterns

Authors: Zeolla Gabriel martin
Comments: 5 Pages.

This paper develops the construction of the Golden Patterns for different prime divisors, the discovery of patterns towards infinity. The discovery of infinite harmony represented in fractal numbers and patterns. The golden pattern works with the simple prime numbers that are known as rough numbers and simple composite number.
Category: Number Theory

[4] viXra:1803.0110 [pdf] submitted on 2018-03-08 06:44:51

Question 440 : Nested Radicals and Trigonometric Formulas

Authors: Edgar Valdebenito
Comments: 4 Pages.

This note presents some trigonometric formulas that involving nested radicals.
Category: Number Theory

[3] viXra:1803.0105 [pdf] submitted on 2018-03-07 21:22:05

Göttlers' Proof of the Collatz Conjecture

Authors: Henry Göttler, Chantal Göttler, Heinrich Göttler, Thorsten Göttler, Pei-jung Wu
Comments: 7 Pages. Proof of Collatz Conjecture

Over 80 years ago, the German mathematician Lothar Collatz formulated an interesting mathematical problem, which he was afraid to publish, for the simple reason that he could not solve it. Since then the Collatz Conjecture has been around under several names and is still unsolved, keeping people addicted. Several famous mathematicians including Richard Guy stating “Dont try to solve this problem”. Paul Erd¨os even said ”Mathematics is not yet ready for such problems” and Shizuo Kakutani joked that the problem was a Cold War invention of the Russians meant to slow the progress of mathematics in the West. We might have finally freed people from this addiction.
Category: Number Theory

[2] viXra:1803.0098 [pdf] submitted on 2018-03-07 09:05:15

3-Golden Pattern

Authors: Zeolla Gabriel martin
Comments: 6 Pages.

This paper develops the divisibility of the so-called Simple Primes numbers-3, the discovery of a pattern to infinity, the demonstration of the inharmonics that are 2,3, and the harmony of 1. The discovery of infinite harmony represented in fractal numbers and patterns. This is a family before the prime numbers. This paper develops a formula to get simple prime number-3 and simple composite number-3 The simple prime numbers-3 is known as the 5-rough numbers.
Category: Number Theory

[1] viXra:1803.0017 [pdf] replaced on 2018-04-03 12:13:21

Zero Application and Synchronization of Prime Numbers. Theorem and Condition of the Twin Primes

Authors: Pablo Hernan Pereyra
Comments: 4 Pages.

A discrete condition for twin prime numbers is established by Wilson's theorem. By synchronization is obtained a linear diophantine equation that implies by Bertrand Chebyshev's theorem the existence of infinite twin prime numbers.
Category: Number Theory