[25] **viXra:1307.0168 [pdf]**
*submitted on 2013-07-30 20:49:13*

**Authors:** Chun-xuan jiang

**Comments:** 11 Pages.

in 1991 jiang proved Fermat last theorem;in 1994 Wiles proved Fermat last theorem

**Category:** Number Theory

[24] **viXra:1307.0167 [pdf]**
*replaced on 2013-08-07 16:04:09*

**Authors:** Marco Ripà

**Comments:** 4 Pages.

An original result about prime numbers and unproved conjectures. In this paper I will show that, if the Goldbach conjecture is true, any prime number greater than 5 can be expressed as the sum of a prime and the double of another (different) prime. A computational analysis shows that the conjecture is true for every prime below 7465626013.

**Category:** Number Theory

[23] **viXra:1307.0148 [pdf]**
*submitted on 2013-07-25 17:22:01*

**Authors:** Edigles Guedes, Raja Rama Gandhi

**Comments:** 4 Pages. Appeared in Bulletin of Mathematical Sciences & Applications

The main objective of this paper is to develop upper and lower bound for the Andrica
conjecture, gaps between primes, using Jacobi elliptic functions.

**Category:** Number Theory

[22] **viXra:1307.0147 [pdf]**
*submitted on 2013-07-25 17:25:06*

**Authors:** Edigles Guedes, Raja Rama Gandhi

**Comments:** 2 Pages. Appeared in Bulletin of Mathematical Sciences & Applications

We proved the asymptotic for Andrica’s conjecture.

**Category:** Number Theory

[21] **viXra:1307.0146 [pdf]**
*submitted on 2013-07-25 17:28:05*

**Authors:** Edigles Guedes, Raja Rama Gandhi

**Comments:** 9 Pages. Appeared in Bulletin of Mathematical Sciences & Applications

We proved the Andrica’s conjecture.

**Category:** Number Theory

[20] **viXra:1307.0145 [pdf]**
*submitted on 2013-07-25 17:30:13*

**Authors:** Edigles Guedes, Raja Rama Gandhi

**Comments:** 4 Pages. Appeared in Bulletin of Mathematical Sciences & Applications

We prove the Cramér's conjecture.

**Category:** Number Theory

[19] **viXra:1307.0144 [pdf]**
*submitted on 2013-07-25 17:41:37*

**Authors:** Edigles Guedes, Raja Rama Gandhi

**Comments:** 10 Pages. Appeared in Asian Journal of Mathematics and Physics

We prove the 12.10 Theorem of Ivic’s Book for Difference between Consecutive Primes without Riemann’s Hypothesis.

**Category:** Number Theory

[18] **viXra:1307.0143 [pdf]**
*submitted on 2013-07-25 17:44:39*

**Authors:** Edigles Guedes, Raja Rama Gandhi

**Comments:** 7 Pages. Appeared in Asian Journal of Mathematics and Physics

We prove a lower bound for differences between consecutive primes.

**Category:** Number Theory

[17] **viXra:1307.0142 [pdf]**
*submitted on 2013-07-25 17:50:12*

**Authors:** Edigles Guedes, Raja Rama Gandhi

**Comments:** 7 Pages. Appeared in Asian Journal of Mathematics and Physics

We prove the Legendre's conjecture.

**Category:** Number Theory

[16] **viXra:1307.0141 [pdf]**
*submitted on 2013-07-25 17:52:14*

**Authors:** Edigles Guedes, Raja Rama Gandhi

**Comments:** 9 Pages. Appeared in Asian Journal of Mathematics and Physics

We prove the Oppermann's conjecture.

**Category:** Number Theory

[15] **viXra:1307.0140 [pdf]**
*submitted on 2013-07-25 18:00:05*

**Authors:** Edigles Guedes, Raja Rama Gandhi

**Comments:** 5 Pages.

We developed a new functional equation and a new integral representation for the Riemann zeta function.

**Category:** Number Theory

[14] **viXra:1307.0139 [pdf]**
*submitted on 2013-07-25 18:02:44*

**Authors:** Edigles Guedes, Raja Rama Gandhi

**Comments:** 3 Pages.

We create new formulas for Riemann-Siegel Integral and Hardy's Z-function.

**Category:** Number Theory

[13] **viXra:1307.0138 [pdf]**
*submitted on 2013-07-25 18:09:14*

**Authors:** Edigles Guedes, Raja Rama Gandhi

**Comments:** 9 Pages.

We use the contradiction method for prove a restricted Lindelöf hypothesis.

**Category:** Number Theory

[12] **viXra:1307.0137 [pdf]**
*submitted on 2013-07-25 18:17:34*

**Authors:** Edigles Guedes, Raja Rama Gandhi, Srinivas Kishan Anapu

**Comments:** 7 Pages. Appeared in Bulletin of Mathematical Sciences & Applications

We create new formulas for proving Lindelof Hypothesis from Zeta Function.

**Category:** Number Theory

[11] **viXra:1307.0104 [pdf]**
*submitted on 2013-07-21 02:09:16*

**Authors:** Julien Laurendeau

**Comments:** 1 Page. I will use a method of mine that I call the infinity statments

In my last paper on the Goldbach conjecture,I encountered a problem with the proof.I will here fix it.

**Category:** Number Theory

[10] **viXra:1307.0087 [pdf]**
*submitted on 2013-07-17 16:13:06*

**Authors:** Germán Paz

**Comments:** 4 Pages. Draft version. // English version of viXra:1307.0051.

In this paper we show the relation that exists between Pascal's Triangle and Legendre's algorithm for calculating the exact amount of prime numbers that are less than a given number.

**Category:** Number Theory

[9] **viXra:1307.0083 [pdf]**
*replaced on 2013-09-06 02:20:08*

**Authors:** Zhen Liu

**Comments:** 20 Pages.

The theorem for equation reconstruction of prime sequence is presented and proved. This theorem is that the prime sequence could have the determined general term formula through diophantine equation reconstruction of prime number. Using the theorem, the Goldbach Conjecture and Twin Primes Conjecture are proved.

**Category:** Number Theory

[8] **viXra:1307.0078 [pdf]**
*replaced on 2013-12-13 03:52:54*

**Authors:** Martin Schlueter

**Comments:** 36 Pages.

Some Formulas and Pattern

**Category:** Number Theory

[7] **viXra:1307.0074 [pdf]**
*submitted on 2013-07-16 18:08:48*

**Authors:** Zbigniew Płotnicki

**Comments:** 71 Pages.

This article contains my Diophantine equations solutions. I am presenting this mathematical work mainly to attract attention to my proof that special relativity is false that you can find on vixra.org under title “Proof that special relativity is false”.

I am presenting this mathematical work mainly to attract attention to my proof that special relativity is false.

I have worked on diophantine solutions for more than two years. I can prove that my work is completely independent from the work of others and that two years ago I had solution to (as I call it) general case for solutions without little Fermat theorem and simple case with little Fermat theorem, which is much more than others achieved, but I didn’t want to publish it until it would be complete. I sent it to the Polish profesors of mathematics and to myself so I really can prove and document that I had it two years ago. I sent it for example on 10/26/2011 to polish full professor PhD. Edmund Puczylowski from Univeristy of Warsaw and I can prove it with my correspondence with him (I gave full content of this document that I sent to him in Appendix 1). I sent also some diophantine solutions (the simplest case with use of little Fermat theorem) to full professor PhD. Jerzy Tiuryn from Univeristy of Warsaw on 02/23/2011 and I can prove it too.

I’ve searched the Internet and found very little work on this matter:

Wolfram – nothing.

Wikipedia: Fermat Last Theorem/Diophantine equations – single special case;

http://cp4space.files.wordpress.com/2012/10/moda-ch12.pdf – that does not define all solutions

But what I’ve seen is that:

There is given really very little solutions in comparison to my solutions,

There are not all solutions of (as I call it) “general” or at least “simple” case of presented equations for the cases like for example: ua^x+wb^y=vc^z

There is not proof that presented solutions are all such (wich I call “complex not derived”) solutions for any case, like for example: ua^x+wb^y=vc^z,

There is not proof when there exist such (complex not derived) solutions,

There are not solutions for simultaneous equations

There are not solutions for rational exponents

As I know work of others contains only case of solution when
SUM_(i=1..n)(c_i/d*a_i^(x_i))=b^z=(SUM_(i=1..n)(c_i/d*l_i^(x_i))^(t*lcm(x)+1)
or even only SUM_(i=1..n)(a_i^(x_i))=b^z=(SUM_(i=1..n)(l_i^(x_i)))^(t*lcm(x)+1)
which is very little. And does not show how to solve equation without solving qz=t*lcm(x)+1, so this algorithm to solve equation has not complexity O(1) while my has O(1).

There is no solution given for any case (especially for general case) to equations that has coefficient not equal to 1 on the right side.

Which all and much more I’ve done in this article.

If my Diophantine equation solutions are not enough I also give a inverse function to Li(n) function. I think it should be enough.

I named this kind of Diophantine equation that I’ve described in this article after my surname, because I need to refere to them in this article.

Finally I can present part of my work. Thanks for reading. I have more and I will publish it in my book that should come out next year.

Please, give me an endorsement on arxiv (on physics, math), if you can. My username on arxiv is at the end of abstract in the document.

(and let me know at my e-mail address which is at first page of the document)

**Category:** Number Theory

[6] **viXra:1307.0051 [pdf]**
*submitted on 2013-07-10 00:09:30*

**Authors:** Germán Paz

**Comments:** 3 Pages. In Spanish. Draft version. // En español.

In this paper we show the relation that exists between Pascal's Triangle and Legendre's algorithm to calculate the exact amount of prime numbers that are less than a given number.

///////////////////

En este documento se muestra la relación que existe entre el Triángulo de Pascal y el algoritmo de Legendre para calcular la cantidad exacta de números primos menores que un número dado.[5] **viXra:1307.0033 [pdf]**
*submitted on 2013-07-06 15:54:08*

**Authors:** J. S. Markovitch

**Comments:** 3 Pages.

Riemann's R-function is shown to alternately under- and over-estimate the number of primes in the intervals defined by the Fibonacci numbers, specifically from the interval [55,89] to the interval [317811,514229].

**Category:** Number Theory

[4] **viXra:1307.0027 [pdf]**
*submitted on 2013-07-05 05:20:47*

**Authors:** Marius Coman

**Comments:** 2 Pages.

To find generic formulas for Carmichael numbers (beside, of course, the formula that defines them) was for long time one of my targets; I already found such a formula, based on Korselt’s criterion; I possible found now another such a formula.

**Category:** Number Theory

[3] **viXra:1307.0015 [pdf]**
*submitted on 2013-07-03 07:21:51*

**Authors:** Marius Coman

**Comments:** 3 Pages.

I was studying recurrences of the form P(n) = P(n - 1) + 2^k – 2, when incidentally I found a chain of 5 primes in arithmetic progression that satisfy this recurrence (8329, 8839, 9349, 9859, 10369). But, interesting, instead of find easily other chains of primes based on this recurrence, I obtained easily such chains (up to AP-6) defining in other way, based on twin primes, the relation between those 5 primes.

**Category:** Number Theory

[2] **viXra:1307.0012 [pdf]**
*submitted on 2013-07-02 14:20:18*

**Authors:** Sebastián Martín Ruiz

**Comments:** 26 Pages.

Un libro para los amantes de los números:
La función de Smarandache aplicada a los números perfectos, congruencias.
También, las funciones prima y coprima de Smarandache
en conexión con expresiones de los números primos.

**Category:** Number Theory

[1] **viXra:1307.0001 [pdf]**
*replaced on 2013-09-05 01:29:52*

**Authors:** Marius Coman

**Comments:** 148 Pages. Written in Romanian. Published by Education Publishing, USA. Copyright 2013 by Marius Coman.

A math encyclopedia of classes of integers, written in Romanian and containing a bilingual summary, Romanian/English.

**Category:** Number Theory