# Number Theory

## 1607 Submissions

 viXra:1607.0569 [pdf] submitted on 2016-07-31 17:30:32

### An Elementary Proof that Beta(3)=pi^3/32

Authors: Hervé G.
Comments: 19 Pages.

It is presented an elementary proof that Beta(3)=Pi^3/32. Beta is the Dirichlet Beta function.
Category: Number Theory

 viXra:1607.0557 [pdf] submitted on 2016-07-30 15:05:24

### Primes as Sums of Irrational Numbers

Authors: Simon Plouffe
Comments: 3 Pages.

An extension of a known result of Ramanujan is used to produce sums with exponential terms that gives a representation of many prime numbers.
Category: Number Theory

 viXra:1607.0551 [pdf] submitted on 2016-07-29 12:19:22

### Proof of Riemann Hypothesis

Authors: Richard Broxley Omeston
Comments: 1 Page.

In this paper I show how the equivalence of the summation of the Móbius function with the Zeta function allows for proof of the Riemann Hypothesis.
Category: Number Theory

 viXra:1607.0536 [pdf] submitted on 2016-07-28 15:35:29

### Formula for Twin Primes

Authors: José de Jesús Camacho Medina
Comments: 1 Page.

The present article shows an unpublished formula to evaluate twin primes, the formula is based on the theorem of Wilson and contains mathematical functions such that greatest common divisor, factorial and floor function.
Category: Number Theory

 viXra:1607.0522 [pdf] submitted on 2016-07-27 10:29:42

### On Finding All Solutions to the Lemoine - Levy Problem

Authors: Matilda Walter
Comments: 3 Pages.

Lemoine - Levy Conjecture, probably the least known of the 'Goldbach Conjectures', states that every positive odd integer > 5 is a sum of a prime and double of a prime. We present a simple sieve procedure for finding all existing solutions to the problem for any given odd number > 5.
Category: Number Theory

 viXra:1607.0468 [pdf] submitted on 2016-07-25 01:02:22

### On a Possible Generalization of Fermat’s Last Theorem

Authors: Dhananjay P. Mehendale
Comments: 3 Pages

This paper proposes a generalised ABC conjecture and assuming its validity settles a generalised version of Fermat’s last theorem.
Category: Number Theory

 viXra:1607.0437 [pdf] submitted on 2016-07-23 12:06:52

### Infinite Arctangent Sums Involving Fibonacci and Lucas Numbers

Authors: Kunle Adegoke
Comments: 15 Pages.

Using a straightforward elementary approach, we derive numerous infinite arctangent summation formulas involving Fibonacci and Lucas numbers. While most of the results obtained are new, a couple of celebrated results appear as particular cases of the more general formulas derived here.
Category: Number Theory

 viXra:1607.0434 [pdf] submitted on 2016-07-23 12:24:01

### Challenge "Proof of the Lehman Expectation".

Authors: Terubumi Honjou
Comments: 7 Pages.

Chapter12. Challenge "proof of the Lehman expectation". A mathematics difficult problem biggest in history.  With the mathematics difficult problem "proof of the Lehman expectation" biggest in history.  I challenge the difficult problem Lehman expectation that rejected the geniuses challenge for 150 years.  It is challenged the mystery of the prime number, a mathematics difficult problem biggest in history, proof of the Lehman expectation.  Neology of the Lehman expectation. A point of intersection that all 0 points are straight.  An elementary particle pulsation principle founds a door of the Lehman expected proof.
Category: Number Theory

 viXra:1607.0400 [pdf] replaced on 2018-04-05 21:50:38

### Dirichlet's Proof of Fermat's Last Theorem for N = 5 is Flawed

Authors: Quang Nguyen Van
Comments: 3 Pages.

Dirichlet's using algorithm is not enough for proving FLT of n = 5.
Category: Number Theory

 viXra:1607.0381 [pdf] submitted on 2016-07-20 11:59:45

### Interesting Facts Concerning Prime Products and Their Relationship to Lorentz-Like Transformations

Authors: Peter Bissonnet
Comments: 10 Pages.

Prime products are analyzed from various points of view, with an emphasis on graphical representation and analysis. A prime product N is determined to have two integer coordinates D and m. These coordinates are related to the solutions of a parabola, as well as to right triangles, in what the author calls a ‘backbone - rib’ representation. A prime number or a prime product fall on three dimensional helices, which can be represented in two dimensions as sets of parallel lines. If a prime or a prime product can be represented by 6s - 1, then helix 1 or H1 is designated; if a prime or a prime product can be represented by 6s + 1, then helix 2 or H2 is designated. The integer s is really a composite number, which can be represented as s = r + n, where r is the row number and n is the grouping number called the complex number, both determined from the two dimensional representation of the double helices. It is also discovered that, due to the mathematical form relating N to D and m, that there must be Lorentz - like transformations between N, D, and m and a new set Nʹ, Dʹ and mʹ; however, the concept of velocity and the speed of light seem out of place in this instance. Nevertheless, the question is asked as to whether or not prime products can be considered to be away to unite relativity and quantum mechanics, which also depends upon integers in a large measure.
Category: Number Theory

 viXra:1607.0360 [pdf] replaced on 2016-10-25 13:27:33

### Proof Bill Hypothesis a Consequence of the Properties of Invariant Identity of a Certain Type (Elementary Aspect).

Authors: Reuven Tint
Comments: 7 Pages.

A variant of the solution with the help of Bill hypothesis direct evidence "Great" Fermat's theorem elementary methods rows. New are "invariant identity" (keyword) and obtained by us in the text, the identity of the work, which allowed directly to solve the FLT, and several others.
Category: Number Theory

 viXra:1607.0359 [pdf] replaced on 2016-07-20 07:41:06

### On Finding All Solutions to the Goldbach Problem for 2N

Authors: Matilda Walter
Comments: 2 Pages.

We present a simple sieve algorithm for finding all existing solutions to the binary Goldbach problem for a given even number 2N > 4.
Category: Number Theory

 viXra:1607.0178 [pdf] submitted on 2016-07-15 06:08:08

### Divide Beal’s Conjecture into Several Parts Gradually to Prove the Beal’s Conjecture

Authors: Zhang Tianshu
Comments: 25 Pages.

In this article, we first classify A, B and C according to their respective odevity, and thereby get rid of two kinds from AX+BY=CZ. Then, affirmed AX+BY=CZ in which case A, B and C have at least a common prime factor by several concrete equalities. After that, proved AX+BY≠CZ in which case A, B and C have not any common prime factor by mathematical induction with the aid of the symmetric relations of positive odd numbers concerned after divide the inequality in four. Finally, reached a conclusion that the Beal’s conjecture holds water via the comparison between AX+BY=CZ and AX+BY≠CZ under the given requirements.
Category: Number Theory

 viXra:1607.0159 [pdf] submitted on 2016-07-13 11:11:18

### Checking if a Number is Prime

Authors: Maaninou Youssef
Comments: 1 Page.

by this theory you can chek any number if it is a prime or not also you can generat a new prime number
Category: Number Theory

 viXra:1607.0087 [pdf] replaced on 2016-07-25 10:05:25

### Induction and Analogy in a Problem of Finite Sums

Authors: Ryan Zielinski
Comments: 84 Pages. This work is licensed under the CC BY 4.0, a Creative Commons Attribution License.

What is a general expression for the sum of the first n integers, each raised to the mth power, where m is a positive integer? Answering this question will be the aim of the paper....We will take the unorthodox approach of presenting the material from the point of view of someone who is trying to solve the problem himself. Keywords: analogy, Johann Faulhaber, finite sums, heuristics, inductive reasoning, number theory, George Polya, problem solving, teaching of mathematics.
Category: Number Theory

 viXra:1607.0072 [pdf] replaced on 2016-07-15 07:54:41

### The Disappointment of the Riemann Hypothesis

Authors: Korn Rakpradit
Comments: 47 Pages.

The opinions of this work are revising, stalking and proving in details the derivation of Riemann Zeta Function and Riemann Hypothesis, which Riemann did roughly for more than 150 years ago without proof, and correcting all mistakes about the boundaries of the integrals that was found and those undefined (and/or multiplied by zero) functional equations which caused very big problems to this Riemann Hypothesis. Proof or disproof of Riemann Hypothesis’s derivation will be very useful for many mathematicians and physicists nowadays because the Hypothesis is widely used in many subjects and works, unaware of risks, thought it is not officially proved right or wrong.
Category: Number Theory

 viXra:1607.0003 [pdf] submitted on 2016-07-01 03:27:48

### Goldbach and Twin Prime Conjectures Implied by Strong Goldbach Number Sequence

Authors: Pingyuan Zhou
Comments: 13 Pages. If so-called strong Goldbach number sequence introduced in this paper is acceptable then the existence of strong Goldbach number sequence will imply both Goldbach and twin prime conjectures.

Abstract: In this note, we present a new and direct appraoch to prove the Goldbach conjecture that if the existence of the limit of (P) = NSGL/2P as P approaches infinity being 1/2 can be confirmed by asymptotic result arising from large-scale observation data for status of (P) then the Goldbach conjecture is true, where P is a prime greater than 3 but NSGL and 2P are separately the largest strong Goldbach number and the largest Goldbach number generated by P. Further, the existence of the limit also implies the twin prime conjecture by means of the existence of good approximate function form to 2(A) such as our introduced C2/A(1/2) as an attempt, which tends to lower order infinitesimal as 1/A approaches infinitesimal, where A = NSGL-P but 2(A) is the density of strong Goldbach numbers generated by distinct twin prime pairs (p,p+2) among all strong Goldbach numbers from P+1 to P+A and C2 is the twin prime constant in the first Hardy-Littlewood conjecture.
Category: Number Theory