[12] **viXra:1506.0198 [pdf]**
*replaced on 2015-09-28 03:39:41*

**Authors:** Reuven Tint, Michael Tint

**Comments:** 34 Pages. Original article is written in Russian.

In the history of mathematics attempts to find common solutions in integers of Diophantine equations were unsuccessful (except iterate through numbers).In this paper, we obtain an algorithm (identity) of recurrent finding countless coprime integer solutions to equations x^4+y^4=a^4+b^4 , x^4=y^4+a^4+b^4 and some arising from these extraordinary consequences.

**Category:** Number Theory

[11] **viXra:1506.0190 [pdf]**
*submitted on 2015-06-26 19:21:21*

**Authors:** Mouhcine Amrar

**Comments:** 4 Pages.

This work is a study of divisibility and these criteria, in which we will give general relationships and divisibility criteria. We begin this work by answering the following question: what conditions should check the digits dialing the number to make it divisible by d? Among the most known and used criteria are the divisibility by 2, 3, 5, 11...

**Category:** Number Theory

[10] **viXra:1506.0189 [pdf]**
*submitted on 2015-06-26 19:25:11*

**Authors:** Mouhcine AMRAR

**Comments:** 4 Pages.

WE GIVE ALL ABOUT PRIME NUMBERS

**Category:** Number Theory

[9] **viXra:1506.0142 [pdf]**
*replaced on 2015-06-22 11:08:28*

**Authors:** Bertrand Wong

**Comments:** 9 Pages.

This paper shows why the non-trivial zeros of the Riemann zeta function ζ will always be on the critical line Re(s) = 1/2 and not anywhere else on the critical strip bounded by Re(s) = 0 and Re(s) = 1, thus affirming the validity of the Riemann hypothesis.

**Category:** Number Theory

[8] **viXra:1506.0121 [pdf]**
*submitted on 2015-06-15 15:35:17*

**Authors:** Jean Pierre Morvan

**Comments:** 16 Pages.

My first proposal for a demonstration goes back to 1997, well before the editions Faber and Faber allot a bonus of 1 million dollars to that which would show the conjecture of Goldbach. Since this date, i proposed different versions on the form,but unchanged on the bottom.
In 1742, the conjecture of Goldbach was “All even number ; writing as the sum of prime numbers”. The number 1 was regarded as a prime number.

**Category:** Number Theory

[7] **viXra:1506.0102 [pdf]**
*submitted on 2015-06-13 11:08:31*

**Authors:** Guacho Perez

**Comments:** 3 Pages.

A simple study on the Goldbach Conjecture and its links to the Prime Number Theorem and Bertrand's Postulate.

**Category:** Number Theory

[6] **viXra:1506.0082 [pdf]**
*replaced on 2016-02-28 21:58:23*

**Authors:** Ihsan Raja Muda Nasution

**Comments:** 1 Page.

In this paper, we delete the zeros in the critical line.

**Category:** Number Theory

[5] **viXra:1506.0066 [pdf]**
*submitted on 2015-06-08 07:01:07*

**Authors:** J. Yun

**Comments:** 1 page

This paper offers a concise proof of Fermat’s Last Theorem using the Euclidean algorithm.

**Category:** Number Theory

[4] **viXra:1506.0048 [pdf]**
*submitted on 2015-06-06 05:02:36*

**Authors:** J. Yun

**Comments:** 1 Page.

This paper offers a concise proof of Beal’s conjecture using the identity.

**Category:** Number Theory

[3] **viXra:1506.0047 [pdf]**
*submitted on 2015-06-06 05:04:27*

**Authors:** J. Yun

**Comments:** 1 Page.

This paper offers a plain proof of Fermat’s Last Theorem using the cosine rule.

**Category:** Number Theory

[2] **viXra:1506.0046 [pdf]**
*submitted on 2015-06-06 05:11:43*

**Authors:** J. Yun

**Comments:** 1 Page.

This paper offers a plain proof of Beal’s conjecture using the cosine rule.

**Category:** Number Theory

[1] **viXra:1506.0041 [pdf]**
*replaced on 2016-01-15 13:16:12*

**Authors:** Jan Pavo Barukčić, Ilija Barukčić

**Comments:** 11 Pages. (C) Jan Pavo Barukčić, Münster and Ilija Barukčić, Jever, Germany, 2015/2016. PUBLISHED April 2016 BY: Journal of Applied Physics and Mathematics vol. 4, no. 4, pp. 686-696. http://dx.doi.org/10.4236/jamp.2016.44085

Today, the division of zero by zero (0/0) is a concept in philosophy, mathematics and physics without a definite solution. On this view, we are left with an inadequate and unsatisfactory situation that we are not allowed to divide zero by zero while the need to divide zero by zero (i. e. divide a tensor component which is equal to zero by another tensor component which is equal to zero) is great. A solution of the philosophically, logically, mathematically and physically far reaching problem of the division of zero by zero (0/0) is still not in sight. The aim of this contribution is to solve the problem of the division of zero by zero (0/0) while relying on Einstein's theory of special relativity. In last consequence, Einstein's theory of special relativity demands the division of zero by zero. Due to Einstein's theory of special relativity it is (0/0) = 1. As we will see, either we must accept the division of zero by zero as possible and defined or we must abandon Einstein's theory of special relativity as refuted.

**Category:** Number Theory