[12] **viXra:1305.0167 [pdf]**
*replaced on 2013-05-29 04:16:31*

**Authors:** Fortuné Alain Junior BACKOULAS

**Comments:** 82 Pages. We recall that this document is in French, an English version will be published shortly

This document contains new methods and tools that allow us to have a new vision on the theory of numbers. Including understanding of prime numbers.
New highly detailed methods have been developed in this paper and thus help to understand how the primes whose mystery has fascinated interacting in the set of integers.
We are sure that the logic we use here will bring more light to the theory of numbers and that has certainly been understood before.
We invite you to read this

**Category:** Number Theory

[11] **viXra:1305.0154 [pdf]**
*replaced on 2013-10-03 19:04:51*

**Authors:** Cristian Dumitrescu

**Comments:** 9 Pages.

In this article I describe a proof of the fact that ZFC cannot decide whether a certain modified Turing machine, or computer (satisfying a certain condition) will ever halt successfully in finite time. The consequences of this fact in relation to the Riemann Hypothesis are presented.

**Category:** Number Theory

[10] **viXra:1305.0149 [pdf]**
*submitted on 2013-05-24 01:55:13*

**Authors:** Marius Coman

**Comments:** 3 Pages.

A simple list of sequences of integers that reveal interesting properties of few subsets of balanced primes.

**Category:** Number Theory

[9] **viXra:1305.0143 [pdf]**
*submitted on 2013-05-23 12:15:00*

**Authors:** Julien Laurendeau

**Comments:** 2 Pages.

Here,I will prove the goldbach conjecture using proof by induction.

**Category:** Number Theory

[8] **viXra:1305.0134 [pdf]**
*submitted on 2013-05-22 15:17:24*

**Authors:** Marius Coman

**Comments:** 4 Pages.

While studying Fermat pseudoprimes I met few interesting generic forms of numbers that have the property to generate chains of primes and pseudoprimes. I list in this paper few such types of chains.

**Category:** Number Theory

[7] **viXra:1305.0116 [pdf]**
*submitted on 2013-05-19 08:30:03*

**Authors:** Julien Laurendeau

**Comments:** 1 Page.

I found a way to prove the goldbach conjecture, but for that I needed to invent three new conjectures to whom,I still haven’t found a proof. I guess,that the person who will prove these three conjectures would be able to prove the Goldbach conjecture.

**Category:** Number Theory

[6] **viXra:1305.0088 [pdf]**
*submitted on 2013-05-15 12:49:43*

**Authors:** Marius Coman

**Comments:** 3 Pages.

A simple list of sequences of products of three numbers, many of them, if not all of them, having probably an infinity of terms that are Fermat pseudoprimes to base 2 with three prime factors.

**Category:** Number Theory

[5] **viXra:1305.0081 [pdf]**
*submitted on 2013-05-13 06:47:57*

**Authors:** Bassam Abdul-Baki

**Comments:** 5 Pages.

In mathematics, Midy's theorem, named after French mathematician E. Midy, is a statement about the decimal expansion of fractions a/p where p is a prime and a/p has a repeating decimal expansion with an even period. If the period of the decimal representation of a/p is 2n, then the digits in the second half of the repeating decimal period are the 9s complement of the corresponding digits in its first half.
The Extended Midy's Theorem states that if the repeating portion of the decimal expansion of a/p is divided into k-digit numbers, then their sum is a multiple of 10^k − 1.

**Category:** Number Theory

[4] **viXra:1305.0079 [pdf]**
*submitted on 2013-05-13 10:57:55*

**Authors:** Marius Coman

**Comments:** 4 Pages.

The applications of the multiples of the number 30 in the study of Fermat pseudoprimes was for a long time one of my favourite subject of study; in this paper I shall list 13 sequences that I discovered, many of them, if not all of them, having probably an infinity of terms that are Carmichael numbers. I posted many of them on OEIS, where I analized more of their attributes; here I’ll just list them, enumerate their first few terms and present few conjectures.

**Category:** Number Theory

[3] **viXra:1305.0023 [pdf]**
*submitted on 2013-05-03 22:43:55*

**Authors:** Ziaul Hassan Serneabat, Nabila Chowdhury, A.K.M. Masud

**Comments:** 13 Pages.

This paper focuses on the simulation of the flexible manufacturing system. Flexible manufacturing systems (FMS) are production systems consisting of identical multipurpose numerically controlled machines (workstations), automated material handling system, tools, load and unload stations, inspection stations, storage areas and a hierarchical control system. The model will prioritize the job and select the best alternative route with multi-criteria scheduling through an approach based on a fuzzy logic. There are three criteria for both the job sequencing and routing with 27 rules. With the help of the rules the sequence of the jobs are done and the best route is selected.

**Category:** Number Theory

[2] **viXra:1305.0021 [pdf]**
*submitted on 2013-05-04 04:05:51*

**Authors:** Chun-Xuan Jiang

**Comments:** 5 Pages.

Theorem .the simplest proof of Fermat last theorem.We have fermat equation x^(4p)-y^(4p)=
z^(4p),where p is odd prime.We prove that if y and z are integer numbers then x,x^4 and x^p are
irrational numbers.

**Category:** Number Theory

[1] **viXra:1305.0020 [pdf]**
*submitted on 2013-05-04 04:11:27*

**Authors:** Chun-Xuan Jiang

**Comments:** 7 Pages.

We have Fermat equation x^(3p)+y^(3p)=z^(3p) where p is odd prime.We prove that if y and z are integers then x,x^3,x^p are irrational numbers.

**Category:** Number Theory