Number Theory

Jiang is Greatest Mathematician to Surpass Gauss

Authors: Chun-xuan jiang
Comments: 11 Pages.

in 1991 jiang proved Fermat last theorem;in 1994 Wiles proved Fermat last theorem
Category: Number Theory

Moutaoikil-Ripà’s Conjecture on Prime Numbers

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

On Andrica’s Conjecture, Cramér’s Conjecture, gaps Between Primes and Jacobi Theta Functions I

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

On Andrica’s Conjecture, Cramér’s Conjecture, gaps Between Primes and Jacobi Theta Functions II: A Simple Proof of Asymptotic for Andrica’s Conjecture

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

On Andrica’s Conjecture, Cramér’s Conjecture, Gaps Between Primes and Jacobi Theta Functions III: a Simple Proof ForAndrica’s Conjecture

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

On Andrica’s Conjecture, Cramér’s Conjecture, gaps Between Primes and Jacobi Theta Functions IV: A Simple Proof for Cramér’s Conjecture

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

On ANDRICA’S Conjecture, CRAMÉR’S Conjecture, Gaps Between Primes and Jacobi Theta Functions V

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

On Andrica’s Conjecture, Cramér’s Conjecture, gaps Between Primes and Jacobi Theta Functions VI

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

An Elementary Proof of LEGENDRE’S Conjecture

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

An Elementary Proof of OPPERMANN’S Conjecture

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

Investigations on the Theory of Riemann Zeta Function I: New Functional Equation, Integral Representation and Laurent Expansion for Riemann’s Zeta Function

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

Investigations on the Theory of Riemann Zeta Function II: On the Riemann-Siegel Integral and Hardy’s Z-Function

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

Investigations on the Theory of Riemann Zeta Function III: A Simple Proof for a Restricted Lindelöf Hypothesis

Authors: Edigles Guedes, Raja Rama Gandhi
Comments: 9 Pages.

We use the contradiction method for prove a restricted Lindelöf hypothesis.
Category: Number Theory

Investigations on the Theory of Riemann Zeta Function III: A Simple Proof for the Lindelöf Hypothesis

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

Legendre's Algorithm and Pascal's Triangle

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

Equation Reconstruction of Prime Sequence

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

Some Formulas and Pattern

Authors: Martin Schlueter
Comments: 36 Pages.

Some Formulas and Pattern
Category: Number Theory

Infinitely Many Solutions of Wide Class of Diophantine Equations

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

Legendre's Algorithm and Pascal's Triangle //// Algoritmo de Legendre y Triángulo de Pascal

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.

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

Riemann's R-Function and the Distribution of Primes

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

A Possible Generic Formula for Carmichael Numbers

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

A Formula Based on Twin Primes that Generates Chains of Primes in Arithmetic Progression

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

Aplicaciones de la Función de Smarandache Y Las Funciones Prima Y Coprima

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

Enciclopedia Matematică a Claselor de Numere Întregi

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