Number Theory

1709 Submissions

[10] viXra:1709.0288 [pdf] submitted on 2017-09-19 04:55:48

Special Rule for Certain Prime Numbers

Authors: Ranganath G. Kulkarni
Comments: 2 Pages.

A quadratic equation for prime numbers is assumed to be true that satisfy the following four rules. Some prime numbers violate these rules. Whereas some non prime numbers satisfy the four rules. They are not prime, therefore to make them violate the fourth rule we need to study how to choose the value of m and n so as make the quadratic equation as the primes generating formula.
Category: Number Theory

[9] viXra:1709.0258 [pdf] submitted on 2017-09-17 13:33:28

Fermat's Theorem. Proof by 2 Operations

Authors: Victor Sorokine
Comments: 2 Pages.

The essence of the contradiction. The hypothetical Fermat's equality is contradictory between the second digits of the factors of the number А.
Category: Number Theory

[8] viXra:1709.0257 [pdf] submitted on 2017-09-17 13:35:16

Fermat's Theorem. Proof by 2 Operations French

Authors: Victor Sorokine
Comments: 2 Pages. French version

The essence of the contradiction. The hypothetical Fermat's equality is contradictory between the second digits of the factors of the number А.
L'égalité de Fermat est contradictoire entre les deuxièmes chiffres des facteurs du nombre A.
Category: Number Theory

[7] viXra:1709.0256 [pdf] submitted on 2017-09-17 13:36:32

Fermat's Theorem. Proof by 2 Operations Russian

Authors: Victor Sorokine
Comments: 2 Pages. Russian version

The essence of the contradiction. The hypothetical Fermat's equality is contradictory between the second digits of the factors of the number А.
Суть противоречия. Равенство Ферма противоречиво по вторым цифрам сомножителей числа А.
Category: Number Theory

[6] viXra:1709.0227 [pdf] submitted on 2017-09-15 05:23:56

A Minor Theorem Related with the Fermat Conjecture

Authors: José Francisco García Juliá
Comments: 2 Pages.

It is obtained a minor theorem related with the Fermat conjecture.
Category: Number Theory

[5] viXra:1709.0128 [pdf] submitted on 2017-09-11 05:10:30

Theorems on Pythagorean Triples and Prime Numbers

Authors: Faisal Amin Yassein Abdelmohssin
Comments: 3 Pages.

Relationships among natural numbers constituting a Pythagorean triple (PT) and between these natural numbers constituting the Pythagorean triples (PTs) and Prime Numbers (PNs) have been found. These relationships are formulated as theorems; first theorem is that the natural numbers constituting a Pythagorean triple (PT) satisfy a certain equation related to sum of their differences; second theorem is that differences of sum of the natural numbers constituting a Pythagorean triple (PT) are prime numbers.
Category: Number Theory

[4] viXra:1709.0092 [pdf] submitted on 2017-09-08 12:19:26

Question 383 : Nonlinear Equation , Euler Numbers , Number Pi

Authors: Edgar Valdebenito
Comments: 4 Pages.

This note presents some formulas for pi.
Category: Number Theory

[3] viXra:1709.0080 [pdf] submitted on 2017-09-07 23:35:34

The Simplest Proving Method of Fermat's Last Theorem

Authors: Haofeng Zhang
Comments: 10 Pages.

Abstract: In this paper the author gives the simplest proving method of Fermat's Last Theorem (FLT) that is just equivalent to the one that Fermat had said there were not enough spaces to write it down but of course not the same one since nobody knows what the proof of Fermat was. The purpose of this paper is not only just to demonstrate the simplest proof but also to illustrate that there are many simple proving methods of FLT that are waited to be found.
Category: Number Theory

[2] viXra:1709.0013 [pdf] submitted on 2017-09-02 03:44:43

Proving Grimm’s Conjecture by Step-by- Step Forming Consecutive Composite Numbers’ Points at the Number Axis(Chinese)

Authors: Zhang Tianshu
Comments: 25 Pages.

Let us regard positive integers which have a common prime factor as a kind, then the positive half line of the number axis consists of infinite many recurring line segments which have same permutations of c kinds of integers’ points, where c≥1. In this article we shall prove Grimm’s conjecture by the method which changes stepwise symbols of each kind of composite numbers’ points at the original number axis, so as to form consecutive composite numbers’ points inside the limited field of proven Legendre- Zhang conjecture as the true.
Category: Number Theory

[1] viXra:1709.0003 [pdf] submitted on 2017-09-01 07:17:32

Affirmative Resolve of Conway’s Problem

Authors: T.Nakashima
Comments: 1 Page.

In this paper, we prove Conway's problem.
Category: Number Theory