[13] **viXra:1509.0231 [pdf]**
*submitted on 2015-09-25 10:40:29*

**Authors:** Ranganath G Kulkarni

**Comments:** 3 Pages.

By using logic functions we can express sign function, rectangular function, box car function and Heaviside function. It is also possible to express the functions such as square wave, triangular wave, sawtooth wave and rectangular wave.

**Category:** Number Theory

[12] **viXra:1509.0208 [pdf]**
*submitted on 2015-09-23 03:35:53*

**Authors:** Reuven Tint, Michael Tint

**Comments:** 12 Pages. Original article is written in Russian

In this article, we'll present and solve problem of Euler: there are countless cuboids whose diagonal all the faces and the main diagonal are integer. Discovered a new feature of three-dimensional complex space (with respect to the metric), wherein the sum of the two sides of the triangle is less than or equal to the third, in particular, on that basis is we obtain a concise version of the proof of the Fermat's Last Theorem.

**Category:** Number Theory

[11] **viXra:1509.0136 [pdf]**
*submitted on 2015-09-15 16:21:03*

**Authors:** Réjean Labrie

**Comments:** 1 Page.

This article is a conjecture of the presence of at least a first number in each of the n + 2 raw slices of n numbers for consecutive numbers from 1 to n * (n + 2).

**Category:** Number Theory

[10] **viXra:1509.0129 [pdf]**
*submitted on 2015-09-15 09:41:54*

**Authors:** Diego Liberati

**Comments:** 1 Page.

A proof of the conjecture is offered

**Category:** Number Theory

[9] **viXra:1509.0128 [pdf]**
*submitted on 2015-09-15 10:17:17*

**Authors:** Diego Liberati

**Comments:** 1 Page.

A proof of the conjecture is offered

**Category:** Number Theory

[8] **viXra:1509.0127 [pdf]**
*submitted on 2015-09-15 08:42:27*

**Authors:** Diego Liberati

**Comments:** 1 Page.

A proof of the conjecture is offered

**Category:** Number Theory

[7] **viXra:1509.0125 [pdf]**
*submitted on 2015-09-15 01:30:11*

**Authors:** Diego Liberati

**Comments:** 1 Page.

An elementary proof of the conjecture is offered

**Category:** Number Theory

[6] **viXra:1509.0124 [pdf]**
*submitted on 2015-09-15 02:02:42*

**Authors:** Diego Liberati

**Comments:** 1 Page.

An elemantary proof of the conjecture is offered

**Category:** Number Theory

[5] **viXra:1509.0123 [pdf]**
*replaced on 2015-09-15 09:09:35*

**Authors:** Diego Liberati

**Comments:** 1 Page.

An elemetary proof of the conjecture is offered

**Category:** Number Theory

[4] **viXra:1509.0122 [pdf]**
*submitted on 2015-09-15 03:09:22*

**Authors:** Diego Liberati

**Comments:** 1 Page.

A proof of the conjecture is offered

**Category:** Number Theory

[3] **viXra:1509.0109 [pdf]**
*submitted on 2015-09-10 15:16:40*

**Authors:** Francois Zinserling

**Comments:** 7 Pages.

Classical primality testing of large numbers requires a number to be rigorously divided by all prime numbers, up to the square root of the number to be tested. This method is time- and resource- consuming for large numbers. Some time is gained by only dividing by prime numbers to determine the factors, but this too falls short where large numbers are tested for which not all the required lower primes are known. The problem becomes no easier when the very next higher prime number is sought, because the entire rigorous process has to be repeated for every number, and the number of calculations increase as the numbers get bigger.
A prime number is a positive integer that can only be fully divided by 1 and itself. Regarding primality, a positive integer can only have 2 states: prime or non-prime. It is one or the other, no inbetweens. If it can be proven that a number is not non-prime, it is inherently proven that it is prime. This is also the basis upon which the Sieve of Eratosthenes works [1].
A method is presented for finding prime numbers, “from the bottom up” thereby allowing the sieve to be expanded as new prime numbers are discovered. The number of calculations required is greatly reduced by using a quadratic relationship.

**Category:** Number Theory

[2] **viXra:1509.0091 [pdf]**
*submitted on 2015-09-08 05:04:36*

**Authors:** Abdelmajid Ben Hadj Salem

**Comments:** 25 Pages. French translation of the English version of the paper ' An Elementary Proof of the BEAL Conjecture. La version anglaise est soumise au journal Integers. Bienvenue à vos commentaires.

En 1997, Andrew Beal avait annoncé la conjecture suivante: Soient A, B,C, m,n, et l des entiers positifs avec m,n,l >2. Si A^m + ^n = C^l alors A, B,et C ont un facteur commun.
Nous commençons par construire le polynôme P(x)=(x-A^m)(x-B^n)(x+C^l)=x^3-px+q avec p,q des entiers qui dépendent de A^m,B^n et C^l. Nous résolvons l'équation x^3-px+q=0 et nous obtenons les trois racines x_1,x_2,x_3 comme fonctions de p,q et d'un paramètre µ. Comme A^m,B^n,-C^l sont les seules racines de x^3-px+q=0, nous discutons les conditions pour que x_1,x_2,x_3 soient des entiers.

**Category:** Number Theory

[1] **viXra:1509.0031 [pdf]**
*replaced on 2015-09-02 10:58:19*

**Authors:** Diego Liberati

**Comments:** 1 Page.

A conjecture is proposed, stronger than many of the existing conjectures that are themselves stronger than Legendre's one

**Category:** Number Theory