[28] **viXra:1605.0311 [pdf]**
*submitted on 2016-05-31 10:35:22*

**Authors:** José de Jesús Camacho Medina

**Comments:** 6 Pages.

This article disseminates a series of formulas that generate primes numbers as a product of the investigations of the author since the year 2011. This document describes general patterns on the entities primales and conceived an order in its distribution.

**Category:** Number Theory

[27] **viXra:1605.0310 [pdf]**
*submitted on 2016-05-31 12:07:57*

**Authors:** Abdelmajid Ben Hadj Salem

**Comments:** 47 Pages. In French. Paper submitted to the Journal Algebra and Number Theory.

The paper gives a complete proof of the conjecture of BEAL followed by some numerical examples.

**Category:** Number Theory

[26] **viXra:1605.0247 [pdf]**
*submitted on 2016-05-24 00:51:23*

**Authors:** Hajime Mashima

**Comments:** 4 Pages.

This is the expectation that "two or more of the natural number 4/n will be represented by the sum of the three unit fractions".

**Category:** Number Theory

[25] **viXra:1605.0245 [pdf]**
*submitted on 2016-05-23 13:23:29*

**Authors:** Terubumi Honjou

**Comments:** 4 Pages.

The new equation by the elementary particle pulsation hypothesis.
Arrow of time turns. In response to it, mass m changes with +1, 0, -1.
Arrow of time turns.
It is the same as the arrow of time of the Schrodinger equation.
Arrow of time turns.
It is the same as a material wave of the elementary particle pulsation hypothesis.
Current physics is always +mc²>0. Elementary particle mass m does not change.
A pulsation principle suggests a super-high-speed change of elementary particle mass m.

**Category:** Number Theory

[24] **viXra:1605.0229 [pdf]**
*replaced on 2016-06-07 15:21:17*

**Authors:** Ricardo Gil

**Comments:** 2 Pages.

As non-trivial Riemann zero's grow larger on the 1/2 critical line so does the distance grow proportionally between 0 and 1. Therefore, a non-trivial Riemann zero will not be outside the critical strip or off of the critical line.My Visual Proof by Automorphism asserts Symmetry. If 1/2 10^13 is inside (0,1) then 1/2 10^100 is inside (0,1). In other words if there is Symmetry about the real axis and Symmetry about the critical line then there is Symmetry between 1/2 10^13 is inside (0,1) and 1/2 10^100 which is inside (0,1).

**Category:** Number Theory

[23] **viXra:1605.0221 [pdf]**
*submitted on 2016-05-21 11:18:19*

**Authors:** Ricardo Gil

**Comments:** 1 Page.

The purpose of this paper is to share a simple way to solve a Sodoku in three steps. (P = NP ).

**Category:** Number Theory

[22] **viXra:1605.0201 [pdf]**
*submitted on 2016-05-19 07:29:23*

**Authors:** Terubumi Honjou

**Comments:** 6 Pages.

Proof (article) for the Lehman expectation by Mr.Dobranju became the topic.
I think. A prime number and an illustration of commentary of the fusion of the physics make up for prism interpretation. (Mr.Dobranju)
Various wavelengths of the material wave appear as light (rainbow) of each color in the horizon (three-dimensional space).
The summary of the article is called 0 points of prism interpretation.
Light is branched into the light of various colors by a prism and is projected on a straight line.
The figure of prime number, physics fusion by the elementary particle pulsation principle is similar to 0 points of prism interpretation.
A material wave and the point of intersection with the horizon (straight line of Lehman) are zero points of the Lehman expectation.
A prime number and elementary particle pulsation principle hypothesis.(2).
(Fusion of a prime number and the physics. )

**Category:** Number Theory

[21] **viXra:1605.0195 [pdf]**
*replaced on 2016-09-01 00:46:59*

**Authors:** A. A. Frempong

**Comments:** 6 Pages. Copyright © by A. A. Frempong

Honorable Pierre de Fermat was truthful. He could have squeezed the proof of his last theorem into a page margin. Fermat's last theorem has been proved on a single page. Three similar versions of the proof are presented, using a single page for each version. The approach used in each proof is exemplified by the following system: If a system functions properly and one wants to determine if the same system will function properly with changes in the system, one will first determine the necessary conditions which allow the system to function properly, and then guided by the necessary conditions, one will determine if the changes will allow the system to function properly. So also, if one wants to prove that there are no solutions for the equation c^n = a^n + b^n when n > 2, one should first determine why there are solutions when n = 2, and note the necessary conditions in the solution for n = 2. The necessary conditions in the solutions for n = 2. will guide one to determine if there are solutions when n > 2.. For the first two versions, the proof is based on the Pythagorean identity (sin x)^2 + (cos x)^2 = 1; and for the third version, on (a^2 + b^2)/c^2 = 1, with n = 2, where a, b, and c are relatively prime positive integers. It is shown by contradiction that the uniqueness of the n = 2 identity excludes all other n-values, n > 2, from satisfying the equation c^n = a^n + b^n. One will first show that if n = 2 , c^n = a^n + b^n holds, noting the necessary conditions in the solution; followed by showing that if n > 2 (n an integer), c^n = a^n + b^n does not hold. For the first version of the proof, the proof began with reference to a right triangle. The second version of the proof began with ratio terms without any reference to a geometric figure. The third version occupies about half of a page. The third version of the proof began without any reference to a geometric figure or ratio terms. The second and third versions confirmed the proof in the first version. Each proof version is very simple, and even high school students can learn it. The approach used in the proof has applications in science, engineering, medicine, research, business, and any properly working system when desired changes are to be made in the system. Perhaps, the proof in this paper is the proof that Fermat wished there were enough margin for it in his paper. With respect to prizes, if the prize for a 150-page proof were $715,000, then the prize for a single page proof (considering the advantages) using inverse proportion, would be $107,250,000.

**Category:** Number Theory

[20] **viXra:1605.0164 [pdf]**
*submitted on 2016-05-14 20:42:59*

**Authors:** Anthony J. Browne

**Comments:** 2 Pages.

I introduce a congruence that restates the characterization of primes that have 2 as a quadratic residue, non-residue.

**Category:** Number Theory

[19] **viXra:1605.0162 [pdf]**
*submitted on 2016-05-15 02:34:43*

**Authors:** Anthony J. Browne

**Comments:** 2 Pages.

This short paper presents a new form of the Liouville function. To the author's best knowledge, this relationship is previously unknown.

**Category:** Number Theory

[18] **viXra:1605.0160 [pdf]**
*submitted on 2016-05-14 14:20:12*

**Authors:** Anthony J. Browne

**Comments:** 2 Pages.

In this short paper I present a closed form formula for the right half of Pascal's triangle.

**Category:** Number Theory

[17] **viXra:1605.0140 [pdf]**
*submitted on 2016-05-13 11:27:31*

**Authors:** José de Jesús Camacho Medina

**Comments:** 2 Pages.

This article disseminates a new mathematical concept designed by the author in the year 2015 to which entitled: "Magic Dart", this mathematical entity has a property exquisite not before discovered by the mathematical community, which will be of great pleasure for those who are interested in the educational and recreational mathematics.
One of the activities that are carried out by the author in his daily work is the teaching practice and it is there where attempts to combine the objectives entrusted to him in the delivery of the classes with the implementation of the Recreational Mathematics, always seeking to expand and disclose in an entertaining way the mathematical knowledge that are manifest in a classroom.

**Category:** Number Theory

[16] **viXra:1605.0134 [pdf]**
*submitted on 2016-05-12 19:39:00*

**Authors:** Terubumi Honjou

**Comments:** 6 Pages.

Online posting to YOUTUBE.
Einstein continued looking for four-dimensional space.
I discovered 4-dimensional space.
I upload it in 2010/09/02.
Contributor excellent Hikari368.
It is 215533 access (as of 2016.5.12).
As the key which realized a general theory, Einstein of later years continued looking for four-dimensional space, but was not able to carry it out. An elementary particle pulsation principle discovered the four-dimensional space. The elementary particle pulsates in the four-dimensional space.

**Category:** Number Theory

[15] **viXra:1605.0131 [pdf]**
*submitted on 2016-05-13 01:10:28*

**Authors:** Terubumi Honjou

**Comments:** 11 Pages.

Online posting to YOUTUBE.
When the mystery of the prime number is removed, the elementary particle pulsation principle will be recognized as the theory of all things.
I assume real number axis, cross axle an imaginary number axis with a vertical axis and insert a figure of elementary particle pulse motion principle energy wave pattern in the complex number coordinate which developed the non-self-evident zero point of a prime number and the zeta function.
I assumed the straight line that 0 points formed a line the horizon which showed the vacuum space of the figure of elementary particle pulsation principle energy wave pattern . I turn a prime number and a figure of that Mr. Sugimoto made which showed 0 points 90 degrees. Non-self-evident straight line and gap 1/2 with the imaginary number axis where 0 points form a line of the zeta function show energy density (zero point energy) of the vacuum space.
I set the top (a mountain and valley) of the wave pattern of the elementary particle pulsation with the prime number on the real number axis. Furthermore, I set it as if a wave pattern passes on a non-self-evident zero point.
I assumed a prime number an orbital pole in a period and assumed a point zero eigenvalue.
The wave (peculiar empty ¬ interval) of the material wave pulsating every 0 points accompanies it. This wave pattern shows elementary particle pulsation, and a minus number particle, a wave pattern do a horizontal state with a wave in the grain ¬ child whom the energy of the place centered on in the heap of wave patterns, the valley of the wave pattern and repeat particle (+mc²), wave (0)¬, conversion (pulsation) of minus number particle (-mc²) super in (Planck time) for a short time.

**Category:** Number Theory

[14] **viXra:1605.0123 [pdf]**
*replaced on 2017-01-14 21:36:03*

**Authors:** Quang Nguyen Van

**Comments:** 4 Pages.

We have spotted an error of Euler's proof,so that the used infinite descent is impossible in his proof (case A).

**Category:** Number Theory

[13] **viXra:1605.0120 [pdf]**
*submitted on 2016-05-11 13:47:07*

**Authors:** Terubumi Honjou

**Comments:** 20 Pages.

The author announced the elementary particle pulsation hypothesis in the Physical Society of Japan of 1980.
To date, I study an elementary particle pulsation hypothesis.
The author contributed the article that let a prime number and physics fuse. youtube (December, 2012).
This page is the gravity in the elementary particle pulsation hypothesis and an article about the electromagnetic force.

**Category:** Number Theory

[12] **viXra:1605.0113 [pdf]**
*replaced on 2016-05-21 11:04:35*

**Authors:** Anthony J. Browne

**Comments:** 6 Pages.

An equivalent form of the Goldbach Conjecture is stated using manipulation of characteristic equations and simple logical arguments that lead to an equation which restates the conjecture. A new form of the number of unordered partitions of an even number into two primes is presented.

**Category:** Number Theory

[11] **viXra:1605.0105 [pdf]**
*submitted on 2016-05-10 13:36:32*

**Authors:** Terubumi Honjo

**Comments:** 20 Pages.

The author announced the elementary particle pulsation hypothesis in the Physical Society of Japan of 1980.
To date, I study an elementary particle pulsation hypothesis.
The author contributed the article that let a prime number and physics fuse. youtube (December, 2012).
This page is the gravity in the elementary particle pulsation hypothesis and an article about the electromagnetic force.

**Category:** Number Theory

[10] **viXra:1605.0104 [pdf]**
*submitted on 2016-05-10 13:58:07*

**Authors:** José de Jesús Camacho Medina

**Comments:** 4 Pages.

This article educational and recreational mathematics, broadcasts a new category of numbers designed by the author in the year 2014 to which I have called "Numbers Fresnillenses" which permeates this title to a sense of belonging because I have is a native from the city of Fresnillo Zacatecas Mexico. This new classification of numbers you have an exquisite property not previously discovered by the mathematical community; it will be a great pleasure for fans of the numbers.

**Category:** Number Theory

[9] **viXra:1605.0103 [pdf]**
*submitted on 2016-05-10 14:09:27*

**Authors:** José de Jesús Camacho Medina

**Comments:** 11 Pages.

This article offers a solution in relation to the distribution of the primes, in this research we provide simple formulas and unpublished with a new approach that allow us to assimilate and conclude that the entities primales are sorted as regular as possible. We provide a new vision for addressing what that since ancient times has been a real challenge for the minds linked to the world mathematician, we deliver the reader a key to unravel the structure and behavior of the primes without open the door to the complexity.

**Category:** Number Theory

[8] **viXra:1605.0095 [pdf]**
*submitted on 2016-05-10 06:59:15*

**Authors:** Terubumi Honjou

**Comments:** 6 Pages.

1) A hypothesis of a prime number and the physics fusion.
The prime number is energy, mcc and a concentric circle. The center is 1/2.
2). The prime number is related deeply with Planck's constant, (h).
3). Natural number is 1* integer. The energy is h X integer.
4). I do it with integer, 1 = 1h.
In m, a radius is a circle of nh. The prime number can express a radius with the circle of the prime number.
5). The equation of the prime number. I accord with energy nh and the prime number of the prime number stairs n turn. (expectation).
6). The prime number distance of the prime number stairs n turn accords with distance of the nuclear resonance energy nh neighborhood. (expectation).

**Category:** Number Theory

[7] **viXra:1605.0082 [pdf]**
*submitted on 2016-05-09 02:55:23*

**Authors:** Jaykov Foukzon

**Comments:** 23 Pages.

In this paper possible completion of the Robinson non-Archimedean field *R constructed by Dedekind sections. As interesting example I show how, a
few simple ideas from non-archimedean analysis on the pseudo-ring *R_d gives a short clear nonstandard reconstruction for the Euler’s original proof of the Goldbach-Euler theorem.

**Category:** Number Theory

[6] **viXra:1605.0066 [pdf]**
*submitted on 2016-05-06 02:22:44*

**Authors:** Terubumi Honjou

**Comments:** 7 Pages.

1)Equations of Euler product multiplied by PI, the equation for the area of a circle.
2) All these equations become concentric.
3) Is the Riemann Zeta function can be represented as a sum of an infinite number of simple sin, cos waves by Fourier transform.
4) And sine curve and cosine curve in circular motion, all in concentric circles that share the same center line.
5) Non-trivial Riemann zero was zero and area of a circle of sin and cosine curve that is equivalent to the Riemann Zeta-function
To be equivalent.
6) And the area of a circle of sine curve and cosine curve to zero all become concentric axis of rotation (1/2 straight).
7) This is Riemann's "line other than zero point does not exist" would prove that. And Honjo expected.

**Category:** Number Theory

[5] **viXra:1605.0061 [pdf]**
*replaced on 2017-07-07 06:39:50*

**Authors:** T.Nakashima

**Comments:** 3 Pages.

This paper is all cycle case resolve.But sequence goes to infinity case I can not prove not possibillity.

**Category:** Number Theory

[4] **viXra:1605.0056 [pdf]**
*submitted on 2016-05-04 11:34:05*

**Authors:** Terubumi Honjou

**Comments:** 3 Pages.

A fusion of prime number and quantum physics.(1)
This figure shows a prime number of the Lehman expectation and the relations with 0 points.
The zeta function is expressed as the sum of simple sin function and cosine function.
The complicated period function is expressed for the sum of sin function and cosine function that are the mathematical expression of a simple wave.

**Category:** Number Theory

[3] **viXra:1605.0010 [pdf]**
*submitted on 2016-05-01 10:14:30*

**Authors:** Reuven Tint

**Comments:** 3 Pages.

Proposed short proof of the fallacy of the ABC assumption
conjecture on the finiteness of the number of "exceptional" triples for r = 2
( "Pythagorean" equation) and other equations, and provides a number of examples.

**Category:** Number Theory

[2] **viXra:1605.0009 [pdf]**
*submitted on 2016-05-01 10:16:44*

**Authors:** Reuven Tint

**Comments:** 3 Pages.

The proof of the fallacy of the assumption of the ABC conjecture. Russian language.

**Category:** Number Theory

[1] **viXra:1605.0008 [pdf]**
*submitted on 2016-05-01 11:42:34*

**Authors:** Terubumi Honjou

**Comments:** 15 Pages.

The hypothesis of the pulsation principle leads a prime number and physical relations.
The horizon and the pulsation wave pattern of the figure of fusion include profound, enormous physical concepts.
The geometry of all things.
A figure of prime number, physical fusion.
I illustrate an uncertainty principle for the first time.
I solve the mystery of the double slit experiment.

**Category:** Number Theory