[27] **viXra:1403.0981 [pdf]**
*submitted on 2014-03-31 16:42:09*

**Authors:** Marius Coman

**Comments:** 3 Pages.

I was playing with randomly formed formulas based on two distinct primes and the difference of them, when I noticed that the formula p + q + 2*(q – p) – 1, where p, q primes, conducts often to a result which is prime, semiprime, square of prime or product of very few primes. Starting from here, I made a conjecture about a way in which any square of a prime seems that can be written. Following from there, I made a conjecture about a possible infinite set of primes, a conjecture regarding the squares of primes and Poulet numbers and yet three other related conjectures.

**Category:** Number Theory

[26] **viXra:1403.0968 [pdf]**
*submitted on 2014-03-29 07:55:34*

**Authors:** Marius Coman

**Comments:** 2 Pages.

In this paper we present four conjectures, one of them regarding a possible infinite sequence of primes and three of them regarding three possible infinite sequences of Poulet numbers, each of them obtained starting from other possible infinite sequence of Poulet numbers.

**Category:** Number Theory

[25] **viXra:1403.0942 [pdf]**
*submitted on 2014-03-26 15:36:59*

**Authors:** A.Garcés Doz

**Comments:** 7 Pages.

Legendre’s conjecture, stated by Adrien-Marie Legendre ( 1752-1833 ), says there is always a prime between n2 and (n+1)2 . This conjecture is part of Landau’s problems. In this paper a proof of this conjecture is presented, using the method of generating prime numbers between consecutive squares, and proving that for every pair of consecutive squares with n >= 3 may be generated at least one prime number that belongs to the interval [n,(n+1)^2]

**Category:** Number Theory

[24] **viXra:1403.0939 [pdf]**
*submitted on 2014-03-26 07:30:09*

**Authors:** Raj C Thiagarajan

**Comments:** 5 Pages. An engineering proof to Beals Conjecture; This paper shows proof and highlights that finding a counter example is not possible due to the intrinsic nature of the equation which will have gcd greater than 1

In this paper, we provide computational results and a proof for Beal’s conjecture. We demonstrate that the common prime factor is intrinsic to this conjecture using the laws of powers. We show that the greatest common divisor is greater than 1 for the Beal’s conjecture.

**Category:** Number Theory

[23] **viXra:1403.0932 [pdf]**
*submitted on 2014-03-25 12:17:13*

**Authors:** Barar Stelian Liviu

**Comments:** 9 Pages.

the method of determining if a number is prime up to a given number .

**Category:** Number Theory

[22] **viXra:1403.0672 [pdf]**
*submitted on 2014-03-23 03:47:33*

**Authors:** Th. Guyer

**Comments:** 1 Page.

A + B = C
Rad(ABC) infinite < C
Number Example: 2*12p2 + 1 = 17p2

**Category:** Number Theory

[21] **viXra:1403.0584 [pdf]**
*submitted on 2014-03-22 01:34:24*

**Authors:** Jozsef Sandor

**Comments:** 5 Pages.

Considerations about the Smarandache, Pseudo-Smarandache, resp. Smarandache-simple functions.

**Category:** Number Theory

[20] **viXra:1403.0444 [pdf]**
*submitted on 2014-03-21 06:05:28*

**Authors:** M. Perez

**Comments:** 6 Pages.

Remarks on some problems regarding Inferior Smarandache Prime Part, Smarandache Prime Base, triple Smarandache function etc.

**Category:** Number Theory

[19] **viXra:1403.0305 [pdf]**
*submitted on 2014-03-19 17:12:04*

**Authors:** Leszek w. Guła

**Comments:** 3 Pages. I woul like to request publish my work.

Elementarny dowód Wielkiego Twierdzenia Fermata (Elementary proof of The Fermat's Last Theorem).

**Category:** Number Theory

[18] **viXra:1403.0302 [pdf]**
*replaced on 2014-03-21 03:08:46*

**Authors:** Shunichi Katoh

**Comments:** 4 Pages. Opportunity for Finding a Simple Proof of FLC.

This paper presents AAC conjecture for a simple and finer version of FLT (Fermat's Last Theorem) which had been FLC (Fermat's Last Conjecture) for more than 350 years since 1637 and was finally proved in the end of the 20th cencury in a profoundly sophisticated and complex way. However complex the proof is, FLC itself is very simple. It conjectures that a simple equation has no solutions. AAC conjecture comes from a pursuit of a simpler proof of FLC. It conjectures that two simple equations have no solutions except some evident ones. It is shown, in a rigorous and step-by-step way, that if AAC is true then FLC is true, and that AAC is a finer version of FLC. AAC conjecture will give us a finer view and an opportunity for finding a simple proof of FLC. If AAC conjecture is proved without using FLT, then AAC theorem will be a theorem for itself, and FLT will be a beautiful specialization of AAC theorem.

**Category:** Number Theory

[17] **viXra:1403.0294 [pdf]**
*submitted on 2014-03-17 17:45:38*

**Authors:** Leszek W. Guła

**Comments:** 3 Pages. Thanks

**Category:** Number Theory

[16] **viXra:1403.0289 [pdf]**
*submitted on 2014-03-17 08:20:44*

**Authors:** Leszek W. Guła

**Comments:** 1 Page. Dedicated to my Parents and my Brother

**Category:** Number Theory

[15] **viXra:1403.0275 [pdf]**
*submitted on 2014-03-16 16:59:21*

**Authors:** Leszek Włodzimierz Guła

**Comments:** 2 Pages. My the short proofs are true.

The short proofs of the Fermat's Last Theorem for even n≥4.

**Category:** Number Theory

[14] **viXra:1403.0274 [pdf]**
*submitted on 2014-03-16 17:36:38*

**Authors:** Leszek Włodzimierz Guła

**Comments:** 3 Pages. My proof is true.

1. The hypothetical Fermat's proof of FLT.
2. Elementary proof of The fermat's Last Theorem.

**Category:** Number Theory

[13] **viXra:1403.0269 [pdf]**
*replaced on 2014-04-13 04:00:40*

**Authors:** Marius Coman

**Comments:** 82 Pages.

It is always difficult to talk about arithmetic, because those who do not know what is about, nor do they understand in few sentences, no matter how inspired these might be, and those who know what is about, do no need to be told what is about.Arithmetic is the branch of mathematics that you keep it in you’re soul and you’re mind not in you’re suitcase or laptop. It also will not help you to gain money (unless you will prove Fermat’s last theorem without using complex numbers or you will prove Beal’s conjecture which is unlikely) but it will give you something more important than that. Part One of this book of collected papers aims to show new applications of Smarandache function in the study of some well known classes of numbers, like prime numbers, Poulet numbers, Carmichael numbers, Sophie Germain primes etc. Beside the well known notions of number theory, we defined in these papers the following new concepts: “Smarandache-Coman divisors of order k of a composite integer n with m prime factors”, “Smarandache-Coman congruence on primes”, “Smarandache-Germain primes”, “Coman-Smarandache criterion for primality”, “Smarandache-Korselt criterion”, “Smarandache-Coman constants”. Part Two of this book brings together several articles regarding primes, submitted by the author to the preprint scientific database Vixra.

**Category:** Number Theory

[12] **viXra:1403.0264 [pdf]**
*submitted on 2014-03-14 18:32:50*

**Authors:** Marius Coman

**Comments:** 3 Pages.

In this paper I present the notion of “chameleonic numbers”, a set of composite squarefree numbers not divisible by 2, 3 or 5, having two, three or more prime factors, which have the property that can easily generate primes with a certain formula, other primes than they own prime factors but in an amount proportional with the amount of these ones.

**Category:** Number Theory

[11] **viXra:1403.0230 [pdf]**
*submitted on 2014-03-15 03:25:48*

**Authors:** Marius Coman

**Comments:** 1 Page.

In this paper I present a conjecture about primes with an extremely simple enunciation, but very interesting despite (or on the contrary, because of) its simplicity.

**Category:** Number Theory

[10] **viXra:1403.0207 [pdf]**
*submitted on 2014-03-14 06:06:49*

**Authors:** Krassimir T. Atanassov

**Comments:** 3 Pages.

Treating a problem on Smarandache circular sequence.

**Category:** Number Theory

[9] **viXra:1403.0205 [pdf]**
*submitted on 2014-03-14 06:11:21*

**Authors:** Mladen V. Vassilev

**Comments:** 4 Pages.

Remarks on a problem regarding Smarandache's simple number.

**Category:** Number Theory

[8] **viXra:1403.0184 [pdf]**
*replaced on 2015-06-22 08:12:02*

**Authors:** T.Nakashima

**Comments:** 5 Pages.

This paper is the answer of the Riemann Hypothesis about the sum of the mebius function.

**Category:** Number Theory

[7] **viXra:1403.0083 [pdf]**
*replaced on 2017-02-08 08:52:53*

**Authors:** Ralf Wüsthofen

**Comments:** 10 Pages. First submission to the Annals of Mathematics on March 24, 2013, LATEST VERSION ON http://vixra.org/abs/1702.0300

This paper presents an elementary and short proof of the strong Goldbach conjecture. Whereas the traditional approaches focus on the control over the distribution of the primes by means of circle method and sieve theory, the proof is based on the constructive properties of the prime numbers, reflecting their multiplicative character within the natural numbers. With an equivalent but more convenient form of the conjecture in mind, we create a structure on the natural numbers. That structure leads to arithmetic identities which immediately imply the conjecture, more precisely, an even strengthened form of it. Moreover, we can achieve further results by generalizing the structuring. Thus, it turns out that the statement of the strong Goldbach conjecture is the special case of a general principle.

**Category:** Number Theory

[6] **viXra:1403.0056 [pdf]**
*submitted on 2014-03-08 07:27:04*

**Authors:** Xu Feng

**Comments:** 2 Pages.

Proof of the Brich and swinnerton-Dyer conjecture

**Category:** Number Theory

[5] **viXra:1403.0054 [pdf]**
*submitted on 2014-03-08 04:54:38*

**Authors:** Xu Feng

**Comments:** 1 Page.

it is on the other mathematical formulas of the prime numbers.

**Category:** Number Theory

[4] **viXra:1403.0051 [pdf]**
*submitted on 2014-03-08 03:06:59*

**Authors:** Xu Feng

**Comments:** 1 Page.

Proof of the Riemann Hypothesis

**Category:** Number Theory

[3] **viXra:1403.0026 [pdf]**
*submitted on 2014-03-05 02:09:31*

**Authors:** Marius Coman

**Comments:** 2 Pages.

In this paper I present a property of a set of primes, interesting not because it has a value for distinguish primes from odd composites, because there are such numbers which also have this property, but because it seems to split the set of primes into two classes – the primes that have this property and the primes that have not this property – containing primes in surprisingly equal proportion.

**Category:** Number Theory

[2] **viXra:1403.0025 [pdf]**
*submitted on 2014-03-05 02:29:58*

**Authors:** Zhang Tianshu

**Comments:** 15 Pages.

If every positive integer is able to be operated into 1 by set operational rule of the Collatz conjecture, then begin with 1, we can get all positive integers by another operational rule on quite the contrary to the set operational rule after pass infinite many operations. Thereby, we try to substitute such a proof of equal value for directly proving the Collatz conjecture by mathematical induction, and achieved our anticipated goal.

**Category:** Number Theory

[1] **viXra:1403.0009 [pdf]**
*replaced on 2015-12-01 11:32:01*

**Authors:** Ameet Sharma

**Comments:** 18 Pages.

We present the proof of the non-existence of points at a rational distance from all 4 corners of a rational length square.

**Category:** Number Theory