[10] **viXra:1211.0122 [pdf]**
*replaced on 2013-03-09 04:49:32*

**Authors:** Eduardo Calooy Roque

**Comments:** 8 Pages.

General formulas for generating sequences of Pythagorean triples ordered by c-b are studied in this paper. As computational proof, tables were made with a C++ script showing Pythagorean triples ordered by c-b and included as text files and screenshots. Furthermore, to enable readers to check and verify them, the C++ script which will interactively generate tables of Pythagorean triples from the computer console command line is attached. It can be run in Cling and ROOT CINT C/C++ interpreters or compiled.

**Category:** Number Theory

[9] **viXra:1211.0116 [pdf]**
*submitted on 2012-11-19 16:27:13*

**Authors:** Germán Paz

**Comments:** 75 Pages. The result in this paper (as well as some other results) has been published in ''General Mathematics Notes''. Journal reference: On the Interval [n,2n]: Primes, Composites and Perfect Powers, General Mathematics Notes, 15(1) (2013), 1-15.

In this paper we prove that the interval $[n,9(n+3)/8]$ contains at least one prime number for every positive integer $n$. In order to achieve our goal, we use a result by Pierre Dusart and we also do manual calculations.

**Category:** Number Theory

[8] **viXra:1211.0115 [pdf]**
*submitted on 2012-11-19 15:26:45*

**Authors:** Germán Paz

**Comments:** 29 Pages. In Spanish. // En español. - Un resumen de este trabajo está disponible en http://www.abcdatos.com/tutoriales/tutorial/v2200.html. Dicho resumen fue realizado por Carlos Giraldo Ospina (Lic. Matemáticas, USC, Cali, Colombia).

En este trabajo se propone una demostración de que existen infinitos números primos de las formas $2p+i$ y $2p-i$, con $p$ primo e $i$ entero positivo impar. Pruebas de teoremas más generales se proponen en los artículos viXra:1202.0061 y viXra:1202.0063. // In this paper we propose a proof that there exist infinitely many prime numbers of the forms $2p+i$ and $2p-i$, where $p$ is a prime number and $i$ is a positive odd integer. Proofs of more general theorems are proposed in the articles viXra:1202.0061 and viXra:1202.0063.

**Category:** Number Theory

[7] **viXra:1211.0102 [pdf]**
*submitted on 2012-11-19 00:58:18*

**Authors:** Nasser Almismari

**Comments:** 9 Pages.

This is a new method to express The power sums of (n^m) as a (m+1)th-degree polynomial equation of n, there is some methods like "Faulhaber's formula" and others gives the solution of the power sums. nevertheless my method is doing the same but it does not depend on Bernoulli numbers or integrals as it is a simple algebraic way giving a polynomial equation and proved in a elementary algebraic logic.

**Category:** Number Theory

[6] **viXra:1211.0078 [pdf]**
*submitted on 2012-11-14 00:34:45*

**Authors:** Farrukh Ataev

**Comments:** 2 Pages.

A new concept of exponential-geometric mean is introduced and its properties are analyzed.

**Category:** Number Theory

[5] **viXra:1211.0064 [pdf]**
*submitted on 2012-11-12 08:51:54*

**Authors:** Cogoni Raffaele

**Comments:** 6 Pages.

It is a procedure to find the prime numbers, in practice it is a simplification
the sieve of Eratosthenes

**Category:** Number Theory

[4] **viXra:1211.0040 [pdf]**
*submitted on 2012-11-07 14:53:07*

**Authors:** Chun-Xuan Jiang

**Comments:** 4 Pages.

Using complex hyperbolic functions of order 4m with 4m-1 variables we prove Fermat last theorem for exponents 4p and p ,where p is an odd prime.We rediscover the Fermat proof. The proof of FLT must be direct.But indirect proof of FLT is disbelieving.

**Category:** Number Theory

[3] **viXra:1211.0035 [pdf]**
*submitted on 2012-11-07 06:01:52*

**Authors:** Chun-Xuan Jiang

**Comments:** 4 Pages.

Using complex hyperbolic functions of order 2n with 2n-1 variables we prove Fermat last theorem for exponents 6p and p,where p is an odd prime.The proof of FLT must be direct.But indirect proof of FLT is disbelieving.

**Category:** Number Theory

[2] **viXra:1211.0022 [pdf]**
*submitted on 2012-11-05 13:01:21*

**Authors:** J. S. Markovitch

**Comments:** 71 Pages.

The Koide formula from physics is modified for use with the reciprocals of primes found in the intervals defined by the Fibonacci numbers. This formula's resultant values are found to alternate lower, higher, lower, higher, etc. from the interval (5,8] to the interval (514229,832040]. This pattern, inverted, is also shown to occur when the corresponding results are computed for non-primes.

**Category:** Number Theory

[1] **viXra:1211.0006 [pdf]**
*submitted on 2012-11-02 20:44:40*

**Authors:** Chun-Xuan Jiang

**Comments:** 6 Pages.

Using complex hyperbolic function we prove Fermat last theorem for exponents 3p and p,where p is an odd prime.

**Category:** Number Theory