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2018 - 1801(32) - 1802(22) - 1803(23) - 1804(28) - 1805(33) - 1806(17) - 1807(19) - 1808(15) - 1809(13)

Any replacements are listed farther down

[1845] **viXra:1809.0351 [pdf]**
*submitted on 2018-09-17 17:16:10*

**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

[1844] **viXra:1809.0341 [pdf]**
*submitted on 2018-09-16 11:10:33*

**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

[1843] **viXra:1809.0340 [pdf]**
*submitted on 2018-09-16 12:48:43*

**Authors:** Pedro Hugo García Peláez

**Comments:** 12 Pages.

When dividing any number between 1.618033 we obtain decimal numbers with a period of 1618032 decimals

**Category:** Number Theory

[1842] **viXra:1809.0338 [pdf]**
*submitted on 2018-09-16 13:40:39*

**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

[1841] **viXra:1809.0322 [pdf]**
*submitted on 2018-09-15 10:35:14*

**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

[1840] **viXra:1809.0317 [pdf]**
*submitted on 2018-09-15 19:51:43*

**Authors:** Pedro Hugo García Peláez

**Comments:** Pages.

Al dividir cualquier número entre 1,618033 obtenemos números decimales con un periodo de 1,618032 decimales

**Category:** Number Theory

[1839] **viXra:1809.0207 [pdf]**
*submitted on 2018-09-10 14:02:28*

**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

[1838] **viXra:1809.0158 [pdf]**
*submitted on 2018-09-07 14:10:16*

**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

[1837] **viXra:1809.0139 [pdf]**
*submitted on 2018-09-08 05:07:23*

**Authors:** Ryujin Choe

**Comments:** 1 Page.

Solution of Goldbach's Conjecture

**Category:** Number Theory

[1836] **viXra:1809.0086 [pdf]**
*submitted on 2018-09-04 16:35:05*

**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

[1835] **viXra:1809.0060 [pdf]**
*submitted on 2018-09-03 15:11:34*

**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

[1834] **viXra:1809.0059 [pdf]**
*submitted on 2018-09-03 20:40:44*

**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

[1833] **viXra:1809.0008 [pdf]**
*submitted on 2018-09-01 03:59:30*

**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

[1832] **viXra:1808.0635 [pdf]**
*submitted on 2018-08-30 00:59:38*

**Authors:** A.I.Somsikov

**Comments:** 3 Pages. -

The solution of the problem of irrational numbers is proposed

**Category:** Number Theory

[1831] **viXra:1808.0634 [pdf]**
*submitted on 2018-08-30 01:07:48*

**Authors:** A.I.Somsikov

**Comments:** 4 Pages. -

"the physical sense" (the logical contents) of complex numbers is revealed.

**Category:** Number Theory

[1830] **viXra:1808.0633 [pdf]**
*submitted on 2018-08-30 01:14:33*

**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

[1829] **viXra:1808.0628 [pdf]**
*submitted on 2018-08-28 07:37:10*

**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

[1828] **viXra:1808.0567 [pdf]**
*submitted on 2018-08-26 17:11:59*

**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

[1827] **viXra:1808.0509 [pdf]**
*submitted on 2018-08-21 08:06:10*

**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

[1826] **viXra:1808.0284 [pdf]**
*submitted on 2018-08-20 01:46:43*

**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

[1825] **viXra:1808.0254 [pdf]**
*submitted on 2018-08-18 07:57:07*

**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

[1824] **viXra:1808.0201 [pdf]**
*submitted on 2018-08-15 22:03:17*

**Authors:** Ihsan Raja Muda Nasution

**Comments:** 2 Pages.

In this paper, we find the axiomatic pattern of prime numbers.

**Category:** Number Theory

[1823] **viXra:1808.0193 [pdf]**
*submitted on 2018-08-14 06:41:55*

**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

[1822] **viXra:1808.0190 [pdf]**
*submitted on 2018-08-14 07:42:35*

**Authors:** Edgar Valdebenito

**Comments:** 5 Pages.

Some remarks on the integral 4.371.1 in G&R table of integrals.

**Category:** Number Theory

[1821] **viXra:1808.0187 [pdf]**
*submitted on 2018-08-14 10:56:08*

**Authors:** Pedro Hugo García Peláez

**Comments:** 40 Pages.

La sucesión formada por la suma de los números naturales intercalados entre dos números de Fibonacci consecutivos tiene ciertas curiosas propiedades.
No sé si la sucesión de Fibonacci tendra infinitos números primos, pero esta sucesión de tres números de Fibonacci genera números que no son primos.
Incluso está formada por fracciones irreducibles lo que hace que se aproxime rápidamente a Phi cuadrado.
Incluyo aplicaciones que sirven para el poker, el mercado de valores o la estadística.

**Category:** Number Theory

[1820] **viXra:1808.0180 [pdf]**
*submitted on 2018-08-15 04:02:30*

**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

[1819] **viXra:1808.0158 [pdf]**
*submitted on 2018-08-12 11:45:22*

**Authors:** Radomir Majkic

**Comments:** 4 Pages.

There is no cuboid with all integer edges and face diagonals.

**Category:** Number Theory

[1818] **viXra:1808.0074 [pdf]**
*submitted on 2018-08-07 02:00:58*

**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

[1817] **viXra:1807.0533 [pdf]**
*submitted on 2018-07-31 08:23:22*

**Authors:** Andrey B. Skrypnik

**Comments:** 2 Pages.

This is the third result of applying Formula of Disjoint Sets of Odd Numbers

**Category:** Number Theory

[1816] **viXra:1807.0512 [pdf]**
*submitted on 2018-07-30 22:07:40*

**Authors:** Andrey B. Skrypnik

**Comments:** 2 Pages.

This is the second result of applying Formula of Disjoint Sets of Odd Numbers

**Category:** Number Theory

[1815] **viXra:1807.0510 [pdf]**
*submitted on 2018-07-31 02:52:22*

**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

[1814] **viXra:1807.0494 [pdf]**
*submitted on 2018-07-30 04:59:52*

**Authors:** Andrey B. Skrypnik

**Comments:** 4 Pages.

This is the first result of applying Formula of Disjoint Sets of Odd Numbers

**Category:** Number Theory

[1813] **viXra:1807.0484 [pdf]**
*submitted on 2018-07-28 07:29:36*

**Authors:** Andrey B. Skrypnik

**Comments:** 4 Pages.

Destroyed another fortress of unproven tasks

**Category:** Number Theory

[1812] **viXra:1807.0397 [pdf]**
*submitted on 2018-07-24 08:45:37*

**Authors:** Edgar Valdebenito

**Comments:** 2 Pages.

This note presents some trigonometric integrals.

**Category:** Number Theory

[1811] **viXra:1807.0396 [pdf]**
*submitted on 2018-07-24 08:49:06*

**Authors:** Edgar Valdebenito

**Comments:** 2 Pages.

This note presents a definite integral related with the Euler-Mascheroni constant.

**Category:** Number Theory

[1810] **viXra:1807.0374 [pdf]**
*submitted on 2018-07-22 12:50:11*

**Authors:** Abhijit Bhattacharjee

**Comments:** 4 Pages.

Finiteness of a nonlinear diphantine equation is proved.

**Category:** Number Theory

[1809] **viXra:1807.0283 [pdf]**
*submitted on 2018-07-15 09:39:24*

**Authors:** Andrey B. Skrypnik

**Comments:** 2 Pages.

This is the third result of applying Formula of Disjoint Sets of Odd Numbers

**Category:** Number Theory

[1808] **viXra:1807.0266 [pdf]**
*submitted on 2018-07-14 05:44:43*

**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

[1807] **viXra:1807.0265 [pdf]**
*submitted on 2018-07-14 05:47:47*

**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

[1806] **viXra:1807.0256 [pdf]**
*submitted on 2018-07-13 06:32:07*

**Authors:** Andrey B. Skrypnik

**Comments:** 2 Pages.

This is the second result of applying Formula of Disjoint Sets of Odd Numbers

**Category:** Number Theory

[1805] **viXra:1807.0182 [pdf]**
*submitted on 2018-07-10 06:58:50*

**Authors:** Andrey B. Skrypnik

**Comments:** 4 Pages.

This is the first result of applying Formula of Disjoint Sets of Odd Numbers

**Category:** Number Theory

[1804] **viXra:1807.0116 [pdf]**
*submitted on 2018-07-04 08:46:12*

**Authors:** Andrey B. Skrypnik

**Comments:** 4 Pages.

Destroyed another fortress of unproven tasks

**Category:** Number Theory

[1803] **viXra:1807.0100 [pdf]**
*submitted on 2018-07-05 03:34:36*

**Authors:** Robert Spoljaric

**Comments:** 1 Page.

Expressing the even perfect numbers as the sum of powers of 2

**Category:** Number Theory

[1802] **viXra:1807.0099 [pdf]**
*submitted on 2018-07-05 04:35:17*

**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

[1801] **viXra:1807.0055 [pdf]**
*submitted on 2018-07-02 12:18:14*

**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

[1800] **viXra:1807.0053 [pdf]**
*submitted on 2018-07-02 16:18:53*

**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

[1799] **viXra:1807.0048 [pdf]**
*submitted on 2018-07-03 02:58:32*

**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

[1798] **viXra:1806.0427 [pdf]**
*submitted on 2018-06-29 05:37:45*

**Authors:** Pedro Hugo García Peláez

**Comments:** 3 Pages.

The sum of the numbers interspersed between two Fibonacci numbers has a curious property. The Fibonacci numbers act as border points of subsets of numbers that have a curious property.

**Category:** Number Theory

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

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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

[1780] **viXra:1805.0443 [pdf]**
*submitted on 2018-05-25 04:29:03*

**Authors:** jean pierre MORVAN

**Comments:** 4 Pages.

Why the guess of COLLATZ is the true

**Category:** Number Theory

[1779] **viXra:1805.0431 [pdf]**
*submitted on 2018-05-23 17:07:06*

**Authors:** Zeolla Gabriel Martín

**Comments:** 9 Pages.

The prime numbers greater than 5 have 4 terminations in their unit to infinity (1,3,7,9) and the composite numbers divisible by numbers greater than 3 have 5 terminations in their unit to infinity, these are (1,3,5,7,9). This paper develops an expression to calculate the prime numbers and composite numbers with ending 9.

**Category:** Number Theory

[1778] **viXra:1805.0408 [pdf]**
*submitted on 2018-05-21 07:56:52*

**Authors:** Zhang Tianshu

**Comments:** 15 Pages.

In this article, the author applies the mathematical induction, classifies positive integers, and passes operations according to the operational rule, to achieve the goal that proves the Collatz conjecture finally.

**Category:** Number Theory

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

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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

[882] **viXra:1805.0443 [pdf]**
*replaced on 2018-05-25 07:15:29*

**Authors:** Jean Pierre Morvan

**Comments:** 4 Pages.

Pourquoi la conjecture de COLLATZ est vraie.

**Category:** Number Theory

[881] **viXra:1805.0398 [pdf]**
*replaced on 2018-05-27 19:21:30*

**Authors:** Chris Sloane

**Comments:** 20 Pages.

We discovered a way to write the equation x^n+y^n-z^n=0 first studied by Fermat, in powers of 3 other variables defined as; the sum t = x+y-z, the product (xyz) and another term r = x^2+yz-xt-t^2. Once x^n+y^n-z^n is written in powers of t, r and (xyz) we found that 3 cases of a prime factor q of x^2+yz divided t. We realized that from this alternative form of Fermat’s equation if all cases of q divided t that this would lead to a contradiction and solve Fermat’s Last Theorem. Intrigued by this, we then discover that the fourth case, q=3sp+1 also divides t when using a lemma that uniquely defines an aspect of Fermat’s equation resulting in the following theorem:
If x^p +y^p -z^p =0 and suppose x,y,z are pairwise co- prime then any prime factor q of (x^2 +yz) will divide t ,where t= x+y-z

**Category:** Number Theory