[14] **viXra:1501.0256 [pdf]**
*submitted on 2015-01-31 21:32:13*

**Authors:** Marius Coman

**Comments:** 2 Pages.

In few of my previous papers I defined the MC function. In this paper I make two conjectures, involving this function, the squares of primes and the pairs of twin primes.

**Category:** Number Theory

[13] **viXra:1501.0252 [pdf]**
*replaced on 2015-08-16 20:35:09*

**Authors:** Michael Pogorsky

**Comments:** 9 Pages.

This is one of the versions of proof of the Theorem developed by means of general algebra and based on polynomials a=uwv+v^n; b=uwv+w^n; c=uwv+v^n+w^n and their modifications. The polynomials are deduced as required for a, b, c to satisfy equation a^n+b^n=c^n. The equation also requires existence of positive integers u_p and c_p such that a+b is divisible by (u_p)^n and c is divisible by (c_p)(u_p). Based on these conclusions the contradiction in polynomial equation F(u)=0 is revealed. It proves the Theorem.

**Category:** Number Theory

[12] **viXra:1501.0232 [pdf]**
*submitted on 2015-01-26 17:28:17*

**Authors:** JinHua Fei

**Comments:** 9 Pages.

In this paper, we assume that Hardy-Littlewood Conjecture, we got a better upper bound of the exceptional real zero for a class of module.

**Category:** Number Theory

[11] **viXra:1501.0201 [pdf]**
*replaced on 2015-12-29 19:49:36*

**Authors:** Wu Sheng-Ping

**Comments:** 5 Pages.

The main idea of this article is simply calculating integer
functions in module. The algebraic in the integer modules is studied in
completely new style. By analysis in module and a
careful constructing, a condition of non-solution of Diophantine
Equation $a^p+b^p=c^q$ is proved that:
$(a,b)=(b,c)=1,a,b>0,p,q>12$, $p$ is prime. The proof of this
result is mainly in the last two sections.

**Category:** Number Theory

[10] **viXra:1501.0192 [pdf]**
*submitted on 2015-01-20 04:15:40*

**Authors:** Nicolae Bratu

**Comments:** 13 Pages.

This article generalizes and makes some additions to the method used in this demonstration theorem for exponents 3 and 5. In this regard, this paper presents a complete algebraic demonstration of Fermat’s Last Theorem.

**Category:** Number Theory

[9] **viXra:1501.0150 [pdf]**
*submitted on 2015-01-13 17:48:08*

**Authors:** Marius Coman

**Comments:** 2 Pages.

In a previous paper I defined the MC(x) function in the following way: Let MC(x) be the function defined on the set of odd positive integers with values in the set of primes such that: MC(x) = 1 for x = 1; MC(x) = x, for x prime; for x composite, MC(x) has the value of the prime which results from the following iterative operation: let x = p(1)*p(2)*...*p(n), where p(1),..., p(n) are its prime factors; let y = p(1) + p(2) +...+ p(n) – (n – 1); if y is a prime, then MC(x) = y; if not, then y = q(1)*q(2)*...*q(m), where q(1),..., q(m) are its prime factors; let z = q(1) + q(2) +...+ q(m) – (m – 1); if z is a prime, then MC(x) = z; if not, it is iterated the operation until a prime is obtained and this is the value of MC(x). In this paper I present a property of this function.

**Category:** Number Theory

[8] **viXra:1501.0146 [pdf]**
*submitted on 2015-01-14 01:42:15*

**Authors:** Marius Coman

**Comments:** 3 Pages.

In two of my previous papers, namely “An interesting property of the primes congruent to 1 mod 45 and an ideea for a function” respectively “On the sum of three consecutive values of the MC function”, I defined the MC function. In this paper I present new interesting properties of three Smarandache type sequences analyzed through the MC function.

**Category:** Number Theory

[7] **viXra:1501.0141 [pdf]**
*submitted on 2015-01-13 05:05:44*

**Authors:** Marius Coman

**Comments:** 3 Pages.

In this paper I show a certain property of the primes congruent to 1 mod 45 related to concatenation, namely the following one: concatenating two or three or more of these primes are often obtaied a certain kind of composites, id est composites of the form m*n, where m and n are not necessarily primes, having the property that m + n - 1 is a prime number. Plus, I present an ideea for a function which be interesting to study.

**Category:** Number Theory

[6] **viXra:1501.0129 [pdf]**
*submitted on 2015-01-12 15:53:42*

**Authors:** Ke Xiao

**Comments:** 6 Pages.

Abstract There are many proposed partial prime number formulas, however, no formula can generate all prime numbers. Here we show three formulas which can obtain the entire prime numbers set from the positive integers, based on the Möbius function plus the “omega” function, or the Omega function, or the divisor function.

**Category:** Number Theory

[5] **viXra:1501.0125 [pdf]**
*submitted on 2015-01-12 10:18:33*

**Authors:** Zhang Tianshu

**Comments:** 13 Pages.

We first get rid of three kinds from A+B=C according to their respective odevity and gcf (A, B, C) =1. After that, expound relations between C and raf (ABC) by the symmetric law of odd numbers. Finally we have proven C≤Cε [raf (ABC)] 1+ ε in which case A+B=C, where gcf (A, B, C) =1.

**Category:** Number Theory

[4] **viXra:1501.0121 [pdf]**
*submitted on 2015-01-11 16:01:11*

**Authors:** Marius Coman

**Comments:** 3 Pages.

In this paper I present three functions based on the digital sum of a number which might be interesting to study and ten conjectures. These functions are: (I) F(x) defined as the digital sum of the number 2^x – x^2; (II) G(x) equal to F(x) – x and (III) H(x) defined as the digital sum of the number 2^x + x^2.

**Category:** Number Theory

[3] **viXra:1501.0068 [pdf]**
*submitted on 2015-01-05 06:44:12*

**Authors:** Zhang Tianshu

**Comments:** 12 Pages.

We first get rid of three kinds from A+B=C according to their respective odevity and gcf (A, B, C) =1. After that, expound relations between C and raf (ABC) by the symmetric law of odd numbers. Finally we have proven C≤Cε [raf (ABC)] 1+ ε in which case A+B=C, where gcf (A, B, C) =1.

**Category:** Number Theory

[2] **viXra:1501.0067 [pdf]**
*submitted on 2015-01-05 07:14:57*

**Authors:** Zhang Tianshu

**Comments:** 23 Pages.

First we classify A, B and C according to their respective odevity, and ret rid of two kinds from AX+BY=CZ. Then affirm AX+BY=CZ in which case A, B and C have a common prime factor by concrete examples. After that, prove AX+BY≠CZ in which case A, B and C have not any common prime factor by the mathematical induction with the aid of the symmetric law of odd numbers after the decomposition of the inequality. Finally, we have proven that the Beal’s conjecture holds water after the comparison between AX+BY=CZ and AX+BY≠CZ under the given requirements.

**Category:** Number Theory

[1] **viXra:1501.0050 [pdf]**
*submitted on 2015-01-04 03:48:24*

**Authors:** Maik Becker-Sievert

**Comments:** 1 Page.

Every odd number y is the sum of n following numbers while n is a divisor of y.

**Category:** Number Theory