# Number Theory

## 1808 Submissions

 viXra:1808.0635 [pdf] submitted on 2018-08-30 00:59:38

### Problem of Irrational Numbers

Authors: A.I.Somsikov

The solution of the problem of irrational numbers is proposed
Category: Number Theory

 viXra:1808.0634 [pdf] submitted on 2018-08-30 01:07:48

### Definition of Complex Numbers

Authors: A.I.Somsikov

"the physical sense" (the logical contents) of complex numbers is revealed.
Category: Number Theory

 viXra:1808.0633 [pdf] submitted on 2018-08-30 01:14:33

### Historical Problems of Mathematics. Number and Arithmetic Action

Authors: A.I.Somsikov

The sense (the logical contents) of concept of numbers is revealed. Definition of arithmetic actions is given.
Category: Number Theory

 viXra:1808.0628 [pdf] submitted on 2018-08-28 07:37:10

### Fourier Series - Number Pi - Lerch Function

Authors: Edgar Valdebenito

In this note we recall a formula for pi.The distinctive feature of these formula is that pi is expressed in terms of the Lerch Transcendent Function.
Category: Number Theory

 viXra:1808.0567 [pdf] replaced on 2018-09-05 10:25:08

### A Proof For Beal's Conjecture

Authors: Julian Beauchamp

In the first part of this paper, we show how a^x - b^y can be expressed as a new non-standard binomial formula (to an indeterminate power, n). In the second part, by fixing n to the value of z we compare this binomial formula to the standard binomial formula for c^z to prove the Beal Conjecture.
Category: Number Theory

 viXra:1808.0531 [pdf] replaced on 2019-11-28 02:59:27

### Goldbach's Conjecture

Authors: Toshiro Takami

I proved the Goldbach's conjecture. Even numbers are prime numbers and prime numbers added, but it has not been proven yet whether it can be true even for a huge number (forever huge number). All prime numbers are included in (6n - 1) or (6n + 1) except 2 and 3 (n is a positive integer). All numbers are executed in hexadecimal notation. This does not change even in a huge number (forever huge number). 2 (6n + 2), 4 (6n - 2), 6 (6n) in the figure are even numbers. 1 (6n + 1), 3 (6n + 3), 5 (6n - 1) are odd numbers.
Category: Number Theory

 viXra:1808.0509 [pdf] submitted on 2018-08-21 08:06:10

### Gamma is Irrational

Authors: Timothy W. Jones

We introduce an unaccustomed number system, H±, and show how it can be used to prove gamma is irrational. This number system consists of plus and minus multiplies of the terms of the harmonic series. Using some properties of ln, this system can depict the harmonic series and lim as n goes to infinity of ln n at the same time, giving gamma as an infinite decimal. The harmonic series converges to infinity so negative terms are forced. As all rationals can be given in H± without negative terms, it follows that must be irrational.
Category: Number Theory

 viXra:1808.0284 [pdf] submitted on 2018-08-20 01:46:43

### Discovery of the Prime Number Equation

Authors: Toshiro Takami

【Abstract】 I found a prime number equation. All prime numbers except 2 and 3 are expressed by the following formula. (a = positive integer, t = prime number) For other positive integers, t is an irrational number. As an exception, This generates all prime numbers except 2 and 3, but also generates a composite number of prime numbers. The composite number of the prime has regularity.
Category: Number Theory

 viXra:1808.0254 [pdf] submitted on 2018-08-18 07:57:07

### New Discovery on Golbach Conjecture End Version

Goldbach's famous conjecture has always fascinated eminent mathematicians. In this paper we give a rigorous proof based on a new formulation, namely, that every even integer has a primo-raduis. Our proof is mainly based on the application of Chebotarev-Artin's theorem, Mertens' formula and the Principle exclusion-inclusion of Moivre
Category: Number Theory

 viXra:1808.0201 [pdf] replaced on 2019-08-29 00:31:40

### The Behavior of Primes

Authors: Ihsan Raja Muda Nasution

In this paper, we propose the axiomatic regularity of prime numbers.
Category: Number Theory

 viXra:1808.0190 [pdf] submitted on 2018-08-14 07:42:35

### Gradshteyn and Ryzhik , Page 578 , Integral 4.371.1

Authors: Edgar Valdebenito

Some remarks on the integral 4.371.1 in G&R table of integrals.
Category: Number Theory

 viXra:1808.0180 [pdf] submitted on 2018-08-15 04:02:30

### Equivalent of Brocard's Problem

Authors: Hajime Mashima