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

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**Authors:** T.Nakashima

**Comments:** 1 Page.

In this paper, we prove Conway's problem.

**Category:** Number Theory