# Number Theory

## 1501 Submissions

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

### On the MC Function, the Squares of Primes and the Pairs of Twin Primes

Authors: Marius Coman

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

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

### Proof of the Fermat's Last Theorem

Authors: Michael Pogorsky

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

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

### Hardy-Littlewood Conjecture and Exceptional real Zero

Authors: JinHua Fei

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

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

### High Degree Diophantine Equation by Classical Number Theory

Authors: Wu Sheng-Ping

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

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

### The Fermat's Last Theorem

Authors: Nicolae Bratu

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

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

### On the Sum of Three Consecutive Values of the MC Function

Authors: Marius Coman

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

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

### The MC Function and Three Smarandache Type Sequences, Diophantine Analysis

Authors: Marius Coman

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

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

### An Interesting Property of the Primes Congruent to 1 Mod 45 and an Ideea for a Function

Authors: Marius Coman

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

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

### The Prime Number Formulas

Authors: Ke Xiao

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

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

### A Proof of the Abc Conjecture (After Second Modification)

Authors: Zhang Tianshu

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

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

### Three Functions Based on the Digital Sum of a Number and Ten Conjectures

Authors: Marius Coman

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

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

### A Proof of the Abc Conjecture (After First Modification)

Authors: Zhang Tianshu

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

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

### A Proof of the Beal’s Conjecture (After fifth Modification)

Authors: Zhang Tianshu