Number Theory

1808 Submissions

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

Problem of Irrational Numbers

Authors: A.I.Somsikov
Comments: 3 Pages. -

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

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

Definition of Complex Numbers

Authors: A.I.Somsikov
Comments: 4 Pages. -

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

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

Historical Problems of Mathematics. Number and Arithmetic Action

Authors: A.I.Somsikov
Comments: 10 Pages. -

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

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

Fourier Series - Number Pi - Lerch Function

Authors: Edgar Valdebenito
Comments: 4 Pages.

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

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

A Proof For Beal's Conjecture

Authors: Julian Beauchamp
Comments: 6 Pages.

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

[10] viXra:1808.0531 [pdf] replaced on 2018-09-20 19:53:51

Goldbach's Conjecture Ver.2

Authors: Toshiro Takami
Comments: 15 Pages.

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

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

Gamma is Irrational

Authors: Timothy W. Jones
Comments: 4 Pages.

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

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

Discovery of the Prime Number Equation

Authors: Toshiro Takami
Comments: 9 Pages.

【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

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

New Discovery on Golbach Conjecture End Version

Authors: Bado Idriss Olivier
Comments: 7 Pages.

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

[6] viXra:1808.0201 [pdf] replaced on 2018-08-18 00:13:24

The Distribution of Primes, II

Authors: Ihsan Raja Muda Nasution
Comments: 2 Pages.

In this paper, we find the axiomatic pattern of prime numbers.
Category: Number Theory

[5] viXra:1808.0193 [pdf] replaced on 2018-08-27 07:09:00

Proposal of Solution of the Riemann Hypothesis

Authors: Nicolò Rigamonti
Comments: 7 Pages.

The last version includes an improved and better explanation.
Category: Number Theory

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

Gradshteyn and Ryzhik , Page 578 , Integral 4.371.1

Authors: Edgar Valdebenito
Comments: 5 Pages.

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

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

Equivalent of Brocard's Problem

Authors: Hajime Mashima
Comments: 2 Pages.

Brocard's problem was presented by Henri Brocard in 1876 and 1885. n! + 1 = m2. The number that satisfies this is called "Brown numbers" and three are known: (n;m) = (4; 5); (5; 11); (7:71).
Category: Number Theory

[2] viXra:1808.0158 [pdf] submitted on 2018-08-12 11:45:22

Perfect Cuboid

Authors: Radomir Majkic
Comments: 4 Pages.

There is no cuboid with all integer edges and face diagonals.
Category: Number Theory

[1] viXra:1808.0074 [pdf] submitted on 2018-08-07 02:00:58

A Simple Proof of Fermat's Last Theorem

Authors: Angel Isaac Cruz Escalante
Comments: 3 Pages.

Fermat's last theorem states there are not solutions for a^x+b^x=c^x if (a,b,c,x) are positive integers and x>2, we can consider two possible cases for Fermat's last theorem, when x=4, and x=2n+1, n is natural numbers. case x=4 was proved by Fermat, here is a proof for case x=2n+1.
Category: Number Theory