Number Theory

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Recent submissions

Any replacements are listed farther down

[1841] viXra:1809.0351 [pdf] submitted on 2018-09-17 17:16:10

The Cordiality for the Conjunction of Two Paths

Authors: S.I. Nada, A. Elrokh, R. Hamza
Comments: 16 pages

Abstract A graph is called cordial if it has a 0 - 1 labeling such that the number of vertices (edges) labeled with ones and zeros dier by at most one. The conjunction of two graphs (V1;E1) and (V2;E2) is the graph G = (V;E), where V = V1 x V2 and u = (a1; a2), v = (b1; b2) are two vertices, then uv belongs to E if aibi belongs to Ei for i = 1 or 2. In this paper, we present necessary and sucient condition for cordial labeling for the conjunction of two paths, denoted by Pn ^ Pm. Also, we drive an algorithm to generate cordial labeling for the conjunction Pn ^ Pm.
Category: Number Theory

[1840] viXra:1809.0341 [pdf] submitted on 2018-09-16 11:10:33

Goldbach Pereyra Theorem

Authors: Pablo Hernan Pereyra
Comments: 8 Pages. Copyright 2007

In the present work is demonstrate that the so called Goldbach conjecture from 1742 -- “All positive even numbers greater than two can be expressed as a sum of two primes” – due to Leonhard Euler, is a true statement. This result is partially based on the Wilson theorem, and complementary on our reasoning to cast the problem into a diophantine equation. The latter is the master equation for the conjectures proof.
Category: Number Theory

[1839] viXra:1809.0338 [pdf] submitted on 2018-09-16 13:40:39

A Fast Factoring Algorithm

Authors: Paco Derek Tucker
Comments: 1 Page.

A simple and fast factoring algorithm that requires only copy paste, the modular operation, and paired additive partitions of the number.
Category: Number Theory

[1838] viXra:1809.0322 [pdf] submitted on 2018-09-15 10:35:14

Rough Estimate of Legendre's Conjecture

Authors: Hajime Mashima
Comments: 9 Pages.

Legendre's conjecture argues that there is always a prime number between n2 and (n + 1)2 when natural number n.
Category: Number Theory

[1837] viXra:1809.0207 [pdf] submitted on 2018-09-10 14:02:28

Extension to the Eratosthenes Sieve

Authors: Samia Lakehal
Comments: 13 Pages ; 2 Tables ; 766 Ko

The Sieve of Eratosthenes finds all the prime numbers up to any given limit by eliminating all non-primes from the list of all natural numbers. A list of natural numbers containing no multiples of 2, 3 or 5 is created, it is obtained by 8 formulas. The elimination of non-primes is effectuated from this new list. It then appears that it is possible to express all the non-primes belonging to this list by 36 other formulas, the prime numbers being the numbers satisfying the 8 formulas but not the 36.
Category: Number Theory

[1836] viXra:1809.0158 [pdf] submitted on 2018-09-07 14:10:16

Why the Summation Test Results in a Benford, and not a Uniform Distribution, for Data that Conforms to a Log Normal Distribution

Authors: Robert C. Hall
Comments: 27 Pages.

The Summation test consists of adding all numbers that begin with a particular first digit or first two digits and determining its distribution with respect to these first or first two digits numbers. Most people familiar with this test believe that the distribution is a uniform distribution for any distribution that conforms to Benford's law i.e. the distribution of the mantissas of the logarithm of the data set is uniform U[0,12). The summation test that results in a uniform distribution is true for an exponential function (geometric progression) but not true for a data set that conforms to a Log Normal distribution even when the Log Normal distribution itself closely approximates Benford's Law.
Category: Number Theory

[1835] viXra:1809.0139 [pdf] submitted on 2018-09-08 05:07:23

Solution of Goldbach's Conjecture

Authors: Ryujin Choe
Comments: 1 Page.

Solution of Goldbach's Conjecture
Category: Number Theory

[1834] viXra:1809.0086 [pdf] submitted on 2018-09-04 16:35:05

An Identity for Horadam Sequences

Authors: Kunle Adegoke
Comments: 7 pages, no figures

We derive an identity connecting any two Horadam sequences having the same recurrence relation but whose initial terms may be different. Binomial and ordinary summation identities arising from the identity are developed.
Category: Number Theory

[1833] viXra:1809.0060 [pdf] submitted on 2018-09-03 15:11:34

Elementary Fermat Pereyra Theorem

Authors: Pablo Hernan Pereyra
Comments: 5 Pages. 2009 Copyright

This paper aims to present an elementary demonstration of the Fermat-Wiles theorem, also known as Fermat's Last Theorem, using a different equivalent statement and a parameterization method.
Category: Number Theory

[1832] viXra:1809.0059 [pdf] submitted on 2018-09-03 20:40:44

A Proof of Benfords Law in Geometric Series

Authors: Jeozadaque Marcos
Comments: 4 pages

We show in this paper another proof of Benford’s Law. The idea starts with the problem of to find the first digit of a power. Then we deduced a function to calculate the first digit of any power a j called L f function. The theorem 1.2 its a consequence of the periodicity of the $L_f$ function.
Category: Number Theory

[1831] viXra:1809.0008 [pdf] submitted on 2018-09-01 03:59:30

The Fermat's Last Theorem and Homothetic Solutions

Authors: Radomir Majkic
Comments: 3 Pages.

The minimal homothetic integer solution of the Fermat equation is zero and the Fermat last theorem is true.
Category: Number Theory

[1830] viXra:1808.0635 [pdf] submitted on 2018-08-30 00:59:38

Problem of Irrational Numbers

Authors: A.I.Somsikov
Comments: 3 Pages. -

The solution of the problem of irrational numbers is proposed
Category: Number Theory

[1829] viXra:1808.0634 [pdf] submitted on 2018-08-30 01:07:48

Definition of Complex Numbers

Authors: A.I.Somsikov
Comments: 4 Pages. -

"the physical sense" (the logical contents) of complex numbers is revealed.
Category: Number Theory

[1828] viXra:1808.0633 [pdf] submitted on 2018-08-30 01:14:33

Historical Problems of Mathematics. Number and Arithmetic Action

Authors: A.I.Somsikov
Comments: 10 Pages. -

The sense (the logical contents) of concept of numbers is revealed. Definition of arithmetic actions is given.
Category: Number Theory

[1827] viXra:1808.0628 [pdf] submitted on 2018-08-28 07:37:10

Fourier Series - Number Pi - Lerch Function

Authors: Edgar Valdebenito
Comments: 4 Pages.

In this note we recall a formula for pi.The distinctive feature of these formula is that pi is expressed in terms of the Lerch Transcendent Function.
Category: Number Theory

[1826] viXra:1808.0567 [pdf] submitted on 2018-08-26 17:11:59

A Proof for Beal's Conjecture

Authors: Julian Beauchamp
Comments: 5 Pages.

In the first part of this paper, we show how a^x - b^y can be expressed as a binomial expansion (to an indeterminate power, $z$). In the second part we will show how this leads to a proof for the Beal Conjecture.
Category: Number Theory

[1825] viXra:1808.0509 [pdf] submitted on 2018-08-21 08:06:10

Gamma is Irrational

Authors: Timothy W. Jones
Comments: 4 Pages.

We introduce an unaccustomed number system, H±, and show how it can be used to prove gamma is irrational. This number system consists of plus and minus multiplies of the terms of the harmonic series. Using some properties of ln, this system can depict the harmonic series and lim as n goes to infinity of ln n at the same time, giving gamma as an infinite decimal. The harmonic series converges to infinity so negative terms are forced. As all rationals can be given in H± without negative terms, it follows that must be irrational.
Category: Number Theory

[1824] viXra:1808.0284 [pdf] submitted on 2018-08-20 01:46:43

Discovery of the Prime Number Equation

Authors: Toshiro Takami
Comments: 9 Pages.

【Abstract】 I found a prime number equation. All prime numbers except 2 and 3 are expressed by the following formula. (a = positive integer, t = prime number) For other positive integers, t is an irrational number. As an exception, This generates all prime numbers except 2 and 3, but also generates a composite number of prime numbers. The composite number of the prime has regularity.
Category: Number Theory

[1823] viXra:1808.0254 [pdf] submitted on 2018-08-18 07:57:07

New Discovery on Golbach Conjecture End Version

Authors: Bado Idriss Olivier
Comments: 7 Pages.

Goldbach's famous conjecture has always fascinated eminent mathematicians. In this paper we give a rigorous proof based on a new formulation, namely, that every even integer has a primo-raduis. Our proof is mainly based on the application of Chebotarev-Artin's theorem, Mertens' formula and the Principle exclusion-inclusion of Moivre
Category: Number Theory

[1822] viXra:1808.0201 [pdf] submitted on 2018-08-15 22:03:17

The Distribution of Primes, II

Authors: Ihsan Raja Muda Nasution
Comments: 2 Pages.

In this paper, we find the axiomatic pattern of prime numbers.
Category: Number Theory

[1821] viXra:1808.0193 [pdf] submitted on 2018-08-14 06:41:55

A Thought About the Riemann Hypothesis

Authors: Nicolò Rigamonti
Comments: 7 Pages.

In these papers we will try to face the Riemann hypothesis, basing on the study of the functional equation of the Riemann zeta function.
Category: Number Theory

[1820] viXra:1808.0190 [pdf] submitted on 2018-08-14 07:42:35

Gradshteyn and Ryzhik , Page 578 , Integral 4.371.1

Authors: Edgar Valdebenito
Comments: 5 Pages.

Some remarks on the integral 4.371.1 in G&R table of integrals.
Category: Number Theory

[1819] viXra:1808.0180 [pdf] submitted on 2018-08-15 04:02:30

Equivalent of Brocard's Problem

Authors: Hajime Mashima
Comments: 2 Pages.

Brocard's problem was presented by Henri Brocard in 1876 and 1885. n! + 1 = m2. The number that satisfies this is called "Brown numbers" and three are known: (n;m) = (4; 5); (5; 11); (7:71).
Category: Number Theory

[1818] viXra:1808.0158 [pdf] submitted on 2018-08-12 11:45:22

Perfect Cuboid

Authors: Radomir Majkic
Comments: 4 Pages.

There is no cuboid with all integer edges and face diagonals.
Category: Number Theory

[1817] viXra:1808.0074 [pdf] submitted on 2018-08-07 02:00:58

A Simple Proof of Fermat's Last Theorem

Authors: Angel Isaac Cruz Escalante
Comments: 3 Pages.

Fermat's last theorem states there are not solutions for a^x+b^x=c^x if (a,b,c,x) are positive integers and x>2, we can consider two possible cases for Fermat's last theorem, when x=4, and x=2n+1, n is natural numbers. case x=4 was proved by Fermat, here is a proof for case x=2n+1.
Category: Number Theory

[1816] viXra:1807.0533 [pdf] submitted on 2018-07-31 08:23:22

Proof of the Fourth Landau's Problem (Russian Version)

Authors: Andrey B. Skrypnik
Comments: 2 Pages.

This is the third result of applying Formula of Disjoint Sets of Odd Numbers
Category: Number Theory

[1815] viXra:1807.0512 [pdf] submitted on 2018-07-30 22:07:40

Proof of the Legendre's Conjecture (Russian Version)

Authors: Andrey B. Skrypnik
Comments: 2 Pages.

This is the second result of applying Formula of Disjoint Sets of Odd Numbers
Category: Number Theory

[1814] viXra:1807.0510 [pdf] submitted on 2018-07-31 02:52:22

On the Represenation of Positive Integers by the Sum of Prime Numbers

Authors: Elhadj Zeraoulia
Comments: 11 Pages.

The main objective of this short note is prove that some statements concerning the represenation of positive integers by the sum of prime numbers are equivalent to some true trivial cases. This implies that these statements are also true. The analysis is based on a new prime formula and some trigonometric expressions.
Category: Number Theory

[1813] viXra:1807.0494 [pdf] submitted on 2018-07-30 04:59:52

Proof of the Goldbach's Conjecture (Russian Version)

Authors: Andrey B. Skrypnik
Comments: 4 Pages.

This is the first result of applying Formula of Disjoint Sets of Odd Numbers
Category: Number Theory

[1812] viXra:1807.0484 [pdf] submitted on 2018-07-28 07:29:36

Proof of the Second Landau's Problem (Russian Version)

Authors: Andrey B. Skrypnik
Comments: 4 Pages.

Destroyed another fortress of unproven tasks
Category: Number Theory

[1811] viXra:1807.0397 [pdf] submitted on 2018-07-24 08:45:37

Game of Integrals

Authors: Edgar Valdebenito
Comments: 2 Pages.

This note presents some trigonometric integrals.
Category: Number Theory

[1810] viXra:1807.0396 [pdf] submitted on 2018-07-24 08:49:06

An Interesting Integral

Authors: Edgar Valdebenito
Comments: 2 Pages.

This note presents a definite integral related with the Euler-Mascheroni constant.
Category: Number Theory

[1809] viXra:1807.0374 [pdf] submitted on 2018-07-22 12:50:11

A Note on Diophantine Equation

Authors: Abhijit Bhattacharjee
Comments: 4 Pages.

Finiteness of a nonlinear diphantine equation is proved.
Category: Number Theory

[1808] viXra:1807.0283 [pdf] submitted on 2018-07-15 09:39:24

Proof of the Fourth Landau's Problem

Authors: Andrey B. Skrypnik
Comments: 2 Pages.

This is the third result of applying Formula of Disjoint Sets of Odd Numbers
Category: Number Theory

[1807] viXra:1807.0266 [pdf] submitted on 2018-07-14 05:44:43

Fermat’s Theorem: А+В-С is not a Natural Number

Authors: Victor Sorokine
Comments: 2 Pages.

The study of digits of numbers related to the Fermat's equation shows Fermat's equality is impossible, for n>2.
Category: Number Theory

[1806] viXra:1807.0265 [pdf] submitted on 2018-07-14 05:47:47

Теорема Ферма: А+В-С не является натуральным числом

Authors: Victor Sorokine
Comments: 1 Page. Russian version

Изучение цифр чисел, зависящих от уравнения Теоремы Ферма, показывает, что уравнение невозможно для n>2. The study of digits of numbers related to the Fermat's equation shows Fermat's equality is impossible, for n>2.
Category: Number Theory

[1805] viXra:1807.0256 [pdf] submitted on 2018-07-13 06:32:07

Proof of the Legendre's Conjecture

Authors: Andrey B. Skrypnik
Comments: 2 Pages.

This is the second result of applying Formula of Disjoint Sets of Odd Numbers
Category: Number Theory

[1804] viXra:1807.0182 [pdf] submitted on 2018-07-10 06:58:50

Proof of the Goldbach's Conjecture

Authors: Andrey B. Skrypnik
Comments: 4 Pages.

This is the first result of applying Formula of Disjoint Sets of Odd Numbers
Category: Number Theory

[1803] viXra:1807.0116 [pdf] submitted on 2018-07-04 08:46:12

Proof of the Second Landau's Problem

Authors: Andrey B. Skrypnik
Comments: 4 Pages.

Destroyed another fortress of unproven tasks
Category: Number Theory

[1802] viXra:1807.0100 [pdf] submitted on 2018-07-05 03:34:36

Expressing the Even Perfect Numbers as the Sum of Powers of 2

Authors: Robert Spoljaric
Comments: 1 Page.

Expressing the even perfect numbers as the sum of powers of 2
Category: Number Theory

[1801] viXra:1807.0099 [pdf] submitted on 2018-07-05 04:35:17

The Infinite Sum Series

Authors: Mihir Kumar Jha
Comments: 2 Pages.

The motive of this paper is to put forward a new approach to find the value of infinite sum series, given by S = (1+2+3+4+5+6-----) and to show that, the series converges at the value equal to zero.
Category: Number Theory

[1800] viXra:1807.0055 [pdf] submitted on 2018-07-02 12:18:14

Inverted Sum of the 7-Golden Pattern

Authors: Zeolla Gabriel Martín
Comments: 8 Pages.

This paper develops the divisibility of the so-called Simple Primes numbers (1 to 9), this paper is the continuation of the Golden Pattern. In this summary I will show that the inverted sum ordered by columns maintains amazing equivalences and proportions
Category: Number Theory

[1799] viXra:1807.0053 [pdf] submitted on 2018-07-02 16:18:53

Sum of the First N Factorial Numbers

Authors: Alfredo Olmos hHernández
Comments: 3 Pages.

In this article, we proceed to study and apply the properties of the Gamma function to obtain a formula that allows us to calculate the sum of the first n factorial numbers.
Category: Number Theory

[1798] viXra:1807.0048 [pdf] submitted on 2018-07-03 02:58:32

First Tables of the Inverter, Oct. 1988

Authors: Simon Plouffe
Comments: 48 Pages.

These are scans of my pages of the inverter in 1988, they were done on a Mac 512 with diskettes and paper (about 1 foot thick). The main catalog was on Hypercard. The format at the time was 41 digits in scientific notation and some acronyms for constants ND = golden ratio sqr = sqrt EG = exp(gamma) s = sin c = cos
Category: Number Theory

[1797] viXra:1806.0423 [pdf] submitted on 2018-06-27 07:50:08

The Simplest Proof of the Last Fermat Theorem?

Authors: Victor Sorokine
Comments: 1 Page.

The number D=A^n+B^n-C^n < 0.
Category: Number Theory

[1796] viXra:1806.0422 [pdf] submitted on 2018-06-27 07:51:11

The Simplest Proof of the Last Fermat Theorem? (in Russian)

Authors: Victor Sorokine
Comments: 1 Page. Russian version

Число D=A^n+B^n-C^n < 0.
Category: Number Theory

[1795] viXra:1806.0420 [pdf] submitted on 2018-06-27 08:03:57

Proof of the Last Theorem of Fermat (Russian Version)

Authors: Andrey B. Skrypnik
Comments: 5 Pages.

Here is the only possible Proof of the Last Theorem of the Fermat in the requirements of the Fermat of 1637. - The theorem is proved universally for all numbers. - The theorem is proved on the apparatus of Diofont arithmetic. - The proof takes no more than two notebook pages of handwritten text. - The proof is clear to the pupil of the school. - The real meaning of Fermat's words about the margins of the book page is revealed. The secret of the Last Theorem of Fermat is discovered!
Category: Number Theory

[1794] viXra:1806.0375 [pdf] submitted on 2018-06-26 05:08:21

Proof of the Last Theorem of Fermat

Authors: Andrey B. Skrypnik
Comments: 5 Pages.

Here is the only possible Proof of the Last Theorem of the Fermat in the requirements of the Fermat of 1637. - The theorem is proved universally for all numbers. - The theorem is proved on the apparatus of Diofont arithmetic. - The proof takes no more than two notebook pages of handwritten text. - The proof is clear to the pupil of the school. - The real meaning of Fermat's words about the margins of the book page is revealed. The secret of the Last Theorem of Fermat is discovered!
Category: Number Theory

[1793] viXra:1806.0353 [pdf] submitted on 2018-06-25 02:58:27

(DFC Version 1.0 11 Pages 17.06.2018) a New Conjecture on the Divisor Summatory Function Offering a Much Higher Prediction Accuracy Than Dirichlet's Divisor Problem Approach

Authors: Andrei Lucian Dragoi
Comments: 11 Pages.

This paper presents a new conjecture on the divisor summatory function (also in relation with prime numbers), offering a much higher prediction accuracy than Dirichlet's divisor problem approach. Keywords: conjecture; divisor function; divisor summatory function; prime numbers; Dirichlet's divisor problem
Category: Number Theory

[1792] viXra:1806.0330 [pdf] submitted on 2018-06-22 11:08:32

Queens Puzzle (Russian Version)

Authors: Andrey B. Skrypnik
Comments: 13 Pages.

Complete solution of Queens Puzzle
Category: Number Theory

[1791] viXra:1806.0272 [pdf] submitted on 2018-06-15 11:22:27

Proof of Riemann Hypothesis (Russian Version)

Authors: Andrey B. Skrypnik
Comments: 4 Pages.

Now there is a formula for calculating all primes
Category: Number Theory

[1790] viXra:1806.0219 [pdf] submitted on 2018-06-19 08:57:13

Question 470: Two Integrals

Authors: Edgar Valdebenito
Comments: 2 Pages.

This note presents two integrals.
Category: Number Theory

[1789] viXra:1806.0175 [pdf] submitted on 2018-06-12 09:19:38

Ami: Reconsideration of Axioms for The Real Number

Authors: Yuki Yoshino
Comments: 13 Pages.

The number 0 has no distinction between positive and negative as -0 =+0, it is a number with special properties. In this paper, we define a new concept of numbers that seems to be special, like 0, it's name is Ami.And I propose new axioms of real numbers extended by adding Ami to Hilbert 's real axiom.
Category: Number Theory

[1788] viXra:1806.0095 [pdf] submitted on 2018-06-07 07:25:11

Matrix Individualism Conjectrure

Authors: Vladimir Ushakov
Comments: 1 Page.

The key problem of MIT (matrix individualism theory) is to find a way to fill a square matrix of size N by numbers 1 to N in such a way that no row or column or diagonal contains two equal numbers, diagonal here is any line in matrix with +-45% slope. This definition of diagonal (+-45%) refers only to 1-st order individualism, later I will give a clear definition of higher order matrix individualism as well
Category: Number Theory

[1787] viXra:1806.0062 [pdf] submitted on 2018-06-05 08:43:10

Question 466: an Identity

Authors: Edgar Valdebenito
Comments: 2 Pages.

This note presents a nontrivial identity that involve the number pi: pi=3.1415926535...
Category: Number Theory

[1786] viXra:1806.0061 [pdf] submitted on 2018-06-05 08:46:07

Question 465: Some Integrals , Lambert Function

Authors: Edgar Valdebenito
Comments: 4 Pages.

This note presents some definite integrals.
Category: Number Theory

[1785] viXra:1806.0052 [pdf] submitted on 2018-06-06 02:29:12

Identities for Second Order Recurrence Sequences

Authors: Kunle Adegoke
Comments: 18 Pages.

We derive several identities for arbitrary homogeneous second order recurrence sequences with constant coefficients. The results are then applied to present a harmonized study of six well known integer sequences, namely the Fibonacci sequence, the sequence of Lucas numbers, the Jacobsthal sequence, the Jacobsthal-Lucas sequence, the Pell sequence and the Pell-Lucas sequence.
Category: Number Theory

[1784] viXra:1806.0051 [pdf] submitted on 2018-06-06 02:32:45

Weighted Tribonacci sums

Authors: Kunle Adegoke
Comments: 9 Pages.

We derive various weighted summation identities, including binomial and double binomial identities, for Tribonacci numbers. Our results contain some previously known results as special cases.
Category: Number Theory

[1783] viXra:1806.0046 [pdf] submitted on 2018-06-06 05:11:33

The Ababou Isomorphism Theorem

Authors: S Fushida-Hardy
Comments: 3 Pages.

We construct an isomorphism between the category of Ababou Constants and the category of affine bundles. We explore some special cases, namely the image of the integers equipped with the distinguished Ababou constant under the isomorphism, and prove that the distinguished Ababou constant is composite.
Category: Number Theory

[1782] viXra:1806.0022 [pdf] submitted on 2018-06-02 06:26:51

Precious Primes, a New Category of Primes that May be Used to Represent Three Different Primes: Related Conjecture and Possible Applications Such as Encoding Graphs

Authors: Prashanth R. Rao
Comments: 2 Pages.

In this paper we define a novel kind of prime “p” with "m+n" digits whose first “m” digits represent a prime and the next “n” digits also represent a prime in just one possible way. These primes which we call as precious primes relate three different primes and therefore products of precious primes may allow representation of complex structures such as graphs.
Category: Number Theory

[1781] viXra:1805.0544 [pdf] submitted on 2018-05-31 13:45:07

17-Golden Pattern

Authors: Zeolla Gabriel Martín
Comments: 7 Pages.

This paper develops the divisibility of the so-called Simple Primes numbers-17, the discovery of a pattern to infinity, the demonstration of the inharmonics that are 2,3,5,7,11,13,17 and the harmony of 1. The discovery of infinite harmony represented in fractal numbers and patterns. This is a family before the prime numbers. This paper develops a formula to get simple prime number-17 and simple composite number-17 The simple prime numbers-17 are known as the 19-rough numbers.
Category: Number Theory

Replacements of recent Submissions

[898] viXra:1808.0567 [pdf] replaced on 2018-09-05 10:25:08

A Proof For Beal's Conjecture

Authors: Julian Beauchamp
Comments: 6 Pages.

In the first part of this paper, we show how a^x - b^y can be expressed as a new non-standard binomial formula (to an indeterminate power, n). In the second part, by fixing n to the value of z we compare this binomial formula to the standard binomial formula for c^z to prove the Beal Conjecture.
Category: Number Theory

[897] viXra:1808.0201 [pdf] replaced on 2018-08-18 00:13:24

The Distribution of Primes, II

Authors: Ihsan Raja Muda Nasution
Comments: 2 Pages.

In this paper, we find the axiomatic pattern of prime numbers.
Category: Number Theory

[896] viXra:1808.0193 [pdf] replaced on 2018-08-27 07:09:00

Proposal of Solution of the Riemann Hypothesis

Authors: Nicolò Rigamonti
Comments: 7 Pages.

The last version includes an improved and better explanation.
Category: Number Theory

[895] viXra:1808.0193 [pdf] replaced on 2018-08-17 04:45:35

Proposal of Solution of the Riemann Hypothesis

Authors: Nicolò Rigamonti
Comments: Pages.

In these papers we will try to face the Riemann hypothesis, basing on the study of the functional equation of the Riemann zeta function.
Category: Number Theory

[894] viXra:1807.0510 [pdf] replaced on 2018-08-25 05:18:13

On the Representation of Even Integers by the Sum of Prime Numbers

Authors: Elhadj Zeraoulia
Comments: 13 Pages.

The main objective of this short note is prove that some statements concerning the representation of even integers by the sum of prime numbers are equivalent to some true trivial case. This implies that these statements are also true. The analysis is based on a new prime formula and some trigonometric expressions.
Category: Number Theory

[893] viXra:1807.0116 [pdf] replaced on 2018-07-08 02:27:39

Proof of the Second Landau's Problem

Authors: Andrey B. Skrypnik
Comments: 4 Pages.

Destroyed another fortress of unproven tasks
Category: Number Theory

[892] viXra:1807.0100 [pdf] replaced on 2018-07-14 00:12:41

Which Rows in Pascal’s Triangle Sum to Perfect Numbers?

Authors: Robert Spoljaric
Comments: 2 Pages.

In this note we show which rows in Pascal’s Triangle sum to Perfect Numbers. We end this note with an algorithm allowing us to trivially calculate all the proper divisors for any Perfect Number greater than 6.
Category: Number Theory

[891] viXra:1807.0100 [pdf] replaced on 2018-07-13 02:53:24

Which Rows in Pascal’s Triangle Sum to Perfect Numbers?

Authors: Robert Spoljaric
Comments: 2 Pages.

In this note we show which rows in Pascal’s Triangle sum to Perfect Numbers. We end this note with a conjectured algorithm allowing us to calculate all the proper divisors for any Perfect Number greater than 6.
Category: Number Theory

[890] viXra:1807.0100 [pdf] replaced on 2018-07-09 19:57:01

Which Rows in Pascal’s Triangle Sum to Perfect Numbers?

Authors: Robert Spoljaric
Comments: 2 Pages.

In this note we show which rows in Pascal’s Triangle sum to Perfect Numbers. We end this note with a conjectured algorithm allowing us to calculate all the proper divisors for any Perfect Number greater than 6.
Category: Number Theory

[889] viXra:1807.0100 [pdf] replaced on 2018-07-08 18:53:02

Which Rows in Pascal’s Triangle Sum to Perfect Numbers?

Authors: Robert Spoljaric
Comments: 2 Pages.

In this note we show which rows in Pascal’s Triangle sum to Perfect Numbers.
Category: Number Theory

[888] viXra:1807.0100 [pdf] replaced on 2018-07-08 02:34:08

Which Rows in Pascal’s Triangle Sum to Perfect Numbers?

Authors: Robert Spoljaric
Comments: 2 Pages.

In this note we show which rows in Pascal’s Triangle sum to Perfect Numbers.
Category: Number Theory

[887] viXra:1807.0100 [pdf] replaced on 2018-07-07 05:15:24

Pascal’s Triangle and Perfect Numbers as Sums of Powers of 2

Authors: Robert Spoljaric
Comments: 2 Pages.

In this note we show that the even Perfect Numbers can be found in Pascal’s Triangle by expressing the even Perfect Numbers as sums of powers of 2
Category: Number Theory

[886] viXra:1806.0420 [pdf] replaced on 2018-07-03 11:51:45

Proof of the Last Theorem of Fermat (Russian Version)

Authors: Andrey B. Skrypnik
Comments: 5 Pages.

Here is the only possible Proof of the Last Theorem of the Fermat in the requirements of the Fermat of 1637. - The theorem is proved universally for all numbers. - The theorem is proved on the apparatus of Diofont arithmetic. - The proof takes no more than two notebook pages of handwritten text. - The proof is clear to the pupil of the school. - The real meaning of Fermat's words about the margins of the book page is revealed. The secret of the Last Theorem of Fermat is discovered!
Category: Number Theory

[885] viXra:1806.0046 [pdf] replaced on 2018-06-10 07:22:13

The Ababou Isomorphism Theorem

Authors: Yellocord soc.
Comments: 3 Pages.

We construct an isomorphism between the category of Ababou constants and the category of affine bundles. We explore a special case, namely the image of the integers equipped with the distinguished Ababou constant under the isomorphism. Using our new machinery we prove that the distinguished Ababou constant is composite.
Category: Number Theory

[884] viXra:1806.0022 [pdf] replaced on 2018-06-04 20:47:27

Precious Primes, a New Category of Primes that May be Used to Represent Three Different Primes: Related Conjecture and Possible Applications Such as Encoding Graphs

Authors: Prashanth R. Rao, Tirumal Rao
Comments: 2 Pages.

In this paper we define a novel kind of prime “p” with (m+n) digits whose first “m” digits represent a prime and the next “n” digits also represent a prime in just one possible way. These primes which we call as precious primes relate three different primes and therefore products of precious primes may allow representation of complex structures such as graphs.
Category: Number Theory

[883] viXra:1805.0544 [pdf] replaced on 2018-06-06 19:02:43

17-Golden Pattern

Authors: Zeolla Gabriel Martin
Comments: 10 Pages. The previous file was damaged

This paper develops the divisibility of the so-called Simple Primes numbers-17, the discovery of a pattern to infinity, the demonstration of the inharmonics that are 2,3,5,7,11,13,17 and the harmony of 1. The discovery of infinite harmony represented in fractal numbers and patterns. This is a family before the prime numbers. This paper develops a formula to get simple prime number-17 and simple composite number-17 The simple prime numbers-17 are known as the 19-rough numbers.
Category: Number Theory