# Number Theory

## 1708 Submissions

 viXra:1708.0421 [pdf] submitted on 2017-08-28 08:10:40

### Double Integrals and Series for Some Classical Constants

Authors: Edgar Valdebenito

This note presents a collection of double integrals for some classical constants.
Category: Number Theory

 viXra:1708.0411 [pdf] submitted on 2017-08-28 10:09:24

### Implementation of a Core(c) Number Sieve.

Authors: Preininger Helmut

In this paper we give an implementation of a Core(c) Number Sieve (for a given c=1,2,3,.. we sift out numbers that have in there factorization a prime with a power >= c). For c=2 we have a squarefree number sieve. (Note, that, for c=1, our implementation compute the usual prime number sieve.) Our goal is to use only one codebase and avoid extra algorithms for every c. We use some well known algorithms and adopt it for our purpose.
Category: Number Theory

 viXra:1708.0400 [pdf] submitted on 2017-08-28 00:19:33

### Units and Class Numbers Extracted from Regulators of Small Number Fields

Authors: Lulu Karami

This submission demonstrates how to use the analytic class number formula to express certain quotients of Dedekind's Eta function as a unit raised to the power of a quoteint of class numbers, for particular number fields. It includes a loose derivation for some special cases of reciprocity laws and the Fourier series of particular Eisenstein series.
Category: Number Theory

 viXra:1708.0380 [pdf] replaced on 2017-12-04 09:06:19

### Division by Zero and the Arrival of Ada

Authors: I Gede Putra Yasa ''Gus Satya''

Division by 0 is not defined in mathematics. Mathematics suggests solutions by work around methods. However they give only approximate, not the actual or exact, results. Through this paper we propose methods to solve those problems. One characteristic of our solution methods is that they produce actual or exact results. They are also in conformity with, and supported by, physical or empirical facts. Other characteristic is their simplicity. We can do computations easily based on basic arithmetic or algebra or other computation methods we already familiar with.
Category: Number Theory

 viXra:1708.0255 [pdf] submitted on 2017-08-21 21:17:24

### New Idea of the Goldbach Conjecture

Authors: Jun Chen

A new idea of the Goldbach conjecture has been studied, it is that the even number is more bigger, the average form of the sum of two primes are more larger too. And then, we prove that every sufficiently large even number is the sum of two primes.
Category: Number Theory

 viXra:1708.0234 [pdf] submitted on 2017-08-19 11:06:29

### Fermat's Last Theorem

Authors: Ramaswamy Krishnan

This proof is based on an assumption that value of an infinite series cannot be obtained from a finite number of terms of the series. For all possible factors of (x + y -z) which are not factors of x or y or z, 3 infinite series can be developed, 2 convergent and 1 divergent. In all the 3 cases, the value of the infinite series can be obtained by considering only a finite number of terms. This gives the value for (x + y -z) = p to to the power of alpha * (p1) (p2) (p3). Thus proving Fermat's last theorem.
Category: Number Theory

 viXra:1708.0231 [pdf] submitted on 2017-08-19 11:51:51

### A Relation for Q-Pochhammer Symbol, Q-Bracket, Q-Factorial and Q-Binomial Coefficient.

Authors: Edigles Guedes, Cícera Guedes

In this paper, we construct a relation involving q-Pochhammer symbol, q-bracket, q-factorial and q-binomial coefficient among other things.
Category: Number Theory

 viXra:1708.0230 [pdf] submitted on 2017-08-19 11:56:45

### An Identity for a Q-Hypergeometric Series

Authors: Edigles Guedes, Cícera Guedes

In this paper, we construct a identity for a q-hypergeometric series.
Category: Number Theory

 viXra:1708.0221 [pdf] submitted on 2017-08-19 03:46:20

### Generalization of a Ramanujan Formula

Authors: Mendzina Essomba Francois

I found a formula due to Ramanjan, I have given a generalization in this article
Category: Number Theory

 viXra:1708.0220 [pdf] replaced on 2017-08-23 05:44:34

### Equation for Distribution of Prime Numbers

Authors: Ranganath G. Kulkarni

An equation for distribution of prime numbers is found that agree well with actual values of prime numbers in the range x. We find that Riemann hypothesis may be wrong. We need to study the variation of new variable r with the given number x.
Category: Number Theory

 viXra:1708.0206 [pdf] submitted on 2017-08-17 05:19:11

### 2 to the Power of (p-1) is not Congruent to 1 Mod P Cubed for Any Prime 'p'

Authors: Ramaswamy Krishnan
Comments: 3 Pages. Title has been changed a little bit. Instead of mod p, it should be mod p cubed

Category: Number Theory

 viXra:1708.0204 [pdf] submitted on 2017-08-17 05:25:20

### 3 to the Power of (p-1) is not Congruent to 1 Mod P Cubed if P is Congruent to 1 Mod 6

Authors: Ramaswamy Krishnan

Category: Number Theory

 viXra:1708.0187 [pdf] submitted on 2017-08-16 12:56:13

### Question 273: Nonlinear Equation,Bernoulli Numbers,Number Pi

Authors: Edgar Valdebenito

This note presents some formulas for pi.
Category: Number Theory

 viXra:1708.0181 [pdf] submitted on 2017-08-16 06:53:04

### The Proof of the Lonely Runner Conjecture

Authors: Kurmet Sultan
Comments: 29 pages, Written in Russian

The article presents the proof of the lonely runner conjecture.
Category: Number Theory

 viXra:1708.0177 [pdf] submitted on 2017-08-16 00:48:13

### The Proof of the Collatz Conjecture

Authors: Kurmet Sultan

The article provides with the evidence of the Collatz conjecture.
Category: Number Theory

 viXra:1708.0158 [pdf] submitted on 2017-08-14 08:00:35

### On the Pythagorean Triples (12,y,z)

Authors: Faisal Amin Yassein Abdelmohssin

I found a pattern in the Pythagorean triples formed of the natural number12;{(12,5,13), (12,9,15), (12,16, 20), (12,35,37)}. The pattern is the decreasing value of the difference z - y for the triples such that the differences form a sequence of the even numbers {8,6,4,2} in that order. The existence of such sequence for other natural numbers transforms the Pythagorean equation into a linear equation in y .
Category: Number Theory

 viXra:1708.0141 [pdf] submitted on 2017-08-13 04:27:47

### Yet Another Proof that Zeta(2)=pi^2/6

Authors: Hervé G.

Yet another proof that zeta(2)=Pi^2/6
Category: Number Theory

 viXra:1708.0114 [pdf] submitted on 2017-08-10 21:43:45

### The Binary Goldbach Conjecture: A Proof For the Existence of Prime Sums For All 2N

Authors: Joseph Dise

A minimum number of paired composite sums is shown for all 2N. By logical extension, it proves the existence of paired prime sums for all 2N.
Category: Number Theory

 viXra:1708.0108 [pdf] replaced on 2017-08-12 18:30:40

### The P-alic Numbers

Authors: Antoine Balan
Comments: 2 pages, written in french

We define here a p-adic like field, called the P-alic field. We replace in fact the ring Z by Q[X] and we show a formula of decomposition of a polynomial.
Category: Number Theory

 viXra:1708.0103 [pdf] replaced on 2017-09-24 12:48:05

### The Infinity of Twin Primes

Authors: Joseph Dise

6x±1 are twin primes where x=6nm±(n±m) has no solution for positive integers x, n, and m. This paper follows that definition to its conclusion.
Category: Number Theory

 viXra:1708.0082 [pdf] submitted on 2017-08-08 05:09:33

### New Formulas for Transcendent Functions

Authors: François Mendzina Essomba

I propose new formulas for the transcendent functions that I discovered.
Category: Number Theory

 viXra:1708.0076 [pdf] submitted on 2017-08-08 07:03:16

### Classify Positive Integers to Prove Collatz Conjecture by Mathematical Induction

Authors: Zhang Tianshu

Positive integers which are able to be operated to 1 by set operational rule of the Collatz conjecture and positive integers got via operations by the operational rule versus the set operational rule are one-to-one the same, thus we refer to converse operational routes, apply the mathematical induction, next classify positive integers to prove the Collatz conjecture by substeps according to beforehand prepared two theorems concerned.
Category: Number Theory

 viXra:1708.0063 [pdf] submitted on 2017-08-06 18:22:13

### A Strange Natural Logarithmm Formula

Authors: Mendzina Essomba Francois

A strange formula for the calculation of the natural logarithm of any real number which I guessed almost effortlessly. This formula has the advantage of being very efficient for the calculation of the logarithm of large numbers
Category: Number Theory

 viXra:1708.0048 [pdf] submitted on 2017-08-04 15:49:56

### François Mendzina Essomba Phy Formulae

Authors: Mendzina Essomba Francois

I present some formulas found for the calculation of phy. Some of these formulas accelerate the calculation of decimals and others are written as a function of e and pi by continuous fractions
Category: Number Theory

 viXra:1708.0046 [pdf] submitted on 2017-08-05 03:08:52

### François Mendzina Essomba pi-3.14 Formulae

Authors: Mendzina Essomba Francois