Number Theory

1610 Submissions

[22] viXra:1610.0356 [pdf] submitted on 2016-10-29 14:52:21

A Simple Proof of the Collatz-Gormaund Theorem (Collatz Conjecture)

Authors: Caitherine Gormaund
Comments: 2 Pages.

In which the Collatz Conjecture is proven using fairly simple mathematics.
Category: Number Theory

[21] viXra:1610.0313 [pdf] submitted on 2016-10-26 05:42:56

There Really Are an Infinite Number of Twin Primes, and Other Thoughts on the Distribution of Primes.

Authors: Jared Beal
Comments: 14 Pages.

This paper describes an algorithm for finding all the prime numbers. It also describes how this pattern among primes can be used to show the ratio of primes to not primes in an infinite set of X integers. It can also be used to show that the ratio of twin primes to not twin primes in an infinite set of X integers is always going to be greater than zero.
Category: Number Theory

[20] viXra:1610.0284 [pdf] submitted on 2016-10-24 03:05:49

Доказательство гипотезы Била – следствие свойств инвариантного тождества определенного типа (элементарный аспект)

Authors: Reuven Tint
Comments: Updates: 4.3.2 - 4.3.5.. page 7

Аннотация. Предложен вариант решения гипотезы Била с помощью прямого доказательства» Великой» теоремы Ферма элементарными методами. Новыми являются «инвариантное тождество « (ключевое слово) и полученные нами приведенные в тексте работы тождества, позволившие напрямую решить ВТФ и гипотезу Била,и ряд других. Предложены также новая формулировка теорем ( п.2.1.4.), ,доказательства для n= 1,2,3,..n>2 и x,y,z>2.
Category: Number Theory

[19] viXra:1610.0276 [pdf] submitted on 2016-10-24 00:02:00

On a Question Concerning the Littlewood Violations

Authors: John Smith
Comments: 19 Pages.

Riemann's prime-counting function R(x) looks good for every value of x we can compute, but in the light of Littlewood's result its superiority over li(x) is illusory: Ingram (1938) pointed out that 'for special values of x (as large as we please), the one approximation will deviate as widely as the other from the true value'. This note introduces a type of prime-counting function that is always better than li(x)...
Category: Number Theory

[18] viXra:1610.0275 [pdf] submitted on 2016-10-23 13:15:42

К вопросу о связи эллиптической кривой Фрея с «Великой» теоремой Ферма (элементарный аспект)

Authors: Reuven Tint
Comments: 2 Pages.

Аннотация. Интерес к названной в заглавии проблеме вызван следующими соображениями: 1) Возьмем, к примеру, «пифагорово» уравнение, все взаимно простые решения которого опре- деляются формулами A= a^2- b^2 и B=2ab. Но если мы выберем A≠a^2- b^2 и B≠2ab как гипо- тетически «верные» решения этого уравнения, то, наверное, можно будет доказать, что, в этом случае, «пифагорово» уравнение не существует. Но оно действительно не существует для гипотетически выбранных «верных» решений. 2) Уравнение A^N+B^N = C^N и уравнение эллиптической кривой Фрея (как будет показано ниже для предложенного варианта их решения) не совместны. 3) Поэтому, как представляется, выглядит не совсем убедительной связь между уравнением эллиптической кривой Фрея и соответствующим уравнением Ферма. 4) Приведено приложение.
Category: Number Theory

[17] viXra:1610.0274 [pdf] submitted on 2016-10-23 13:19:39

On the Question of the Relationship of the Elliptic Curve Frey with "Great" Fermat's Theorem (Elementary Aspect).

Authors: Reuven Tint
Comments: 2 Pages.

Annotation. Interest in the title problem is caused by the following considerations: 1) Take, for example, "Pythagoras' equation, all of which are relatively prime solutions determined Delyan formulas A= a^2- b^2 and B=2ab. But if we choose A≠a^2- b^2 and B≠2ab both hypo- Tethyan "correct" solutions of this equation, then perhaps it will be possible to prove that, in this case, "Pythagoras" equation exists. But it really does not exist for the selected hypothetically "true" solutions. 2) The equation A^N+B^N = C^N and the equation of the elliptic curve Frey (as will be shown below for the proposed options to solve them) are not compatible. 3) Therefore, it seems, it does not look quite convincing relationship between the equation elliptic curve Frey Farm and the corresponding equation. 4) Supplement.
Category: Number Theory

[16] viXra:1610.0272 [pdf] submitted on 2016-10-23 13:58:45

Proposal Demonstration of Hypothesis Riemann

Authors: Luca Nascimbene
Comments: 13 Pages.

In this paper the author continue the works [6] [11] [12] and present a proposal for a demonstration on the Riemann Hypothesis and the conjecture on the multiplicity of non-trivial zeros of the Riemann s zeta.
Category: Number Theory

[15] viXra:1610.0253 [pdf] submitted on 2016-10-21 18:17:51

Some Evidencethat the Goldbach Conjecture Could be Proved or Proved False

Authors: Filippos Nikolaidis
Comments: 10 Pages. fil_nikolaidis@yahoo.com

The present study is an effort for giving some evidence that the goldbach conjecture is not true, by showing that not all even natural numbers greater than two can be expressed as a sum of two primes. This conclusion can be drawn by showing that prime numbers are not enough –in population- so that, when added in couples, to give all the even numbers.
Category: Number Theory

[14] viXra:1610.0183 [pdf] submitted on 2016-10-17 05:37:47

Proof of Beal's Conjecture

Authors: Edward Szaraniec
Comments: 5 Pages.

Equation constituting the Beal conjecture is rearranged and squared, then rearranged again and raised to power 4. The result, standing as an equivalent having the same property, is emerging as a singular primitive Pythagorean equation with no solution. So, the conjecture is proved. General line of proving the Pythagorean equation is observed as a moving spirit.
Category: Number Theory

[13] viXra:1610.0172 [pdf] submitted on 2016-10-16 05:13:25

Another Proof for FERMAT’s Last Theorem

Authors: Mugur B. Răuţ
Comments: 5 Pages.

In this paper we propose another proof for Fermat’s Last Theorem (FLT). We found a simpler approach through Pythagorean Theorem, so our demonstration would be close to the times FLT was formulated. On the other hand it seems the Pythagoras’ Theorem was the inspiration for FLT. It resulted one of the most difficult mathematical problem of all times, as it was considered. Pythagorean triples existence seems to support the claims of the previous phrase.
Category: Number Theory

[12] viXra:1610.0106 [pdf] submitted on 2016-10-10 03:35:21

A New 3n-1 Conjecture Akin to Collatz Conjecture

Authors: W.B. Vasantha Kandasamy, K. Ilanthenral, Florentin Smarandache
Comments: 9 Pages.

The Collatz conjecture is an open conjecture in mathematics named so after Lothar Collatz who proposed it in 1937. It is also known as 3n + 1 conjecture, the Ulam conjecture (after Stanislaw Ulam), Kakutani's problem (after Shizuo Kakutani) and so on. In this paper a new conjecture called as the 3n-1 conjecture which is akin to the Collatz conjecture is proposed. It functions on 3n -1, for any starting number n, its sequence eventually reaches either 1, 5 or 17. The 3n-1 conjecture is compared with the Collatz conjecture.
Category: Number Theory

[11] viXra:1610.0099 [pdf] submitted on 2016-10-08 17:28:15

Proof of Sophie Germain Conjecture

Authors: Idriss Olivier Bado
Comments: Dans ce présent document nous donnons la preuve de la conjecture de Sophie Germain en utilisant le theoreme de densité de Chebotarev ,le principe d' inclusion d'exclusion de Moivre ,la formule de Mertens . en 13 pages nous donnons une preuve convaincante

In this paper We give Sophie Germain 's conjecture proof by using Chebotarev density theorem, principle inclusion -exclusion of Moivre, Mertens formula
Category: Number Theory

[10] viXra:1610.0083 [pdf] submitted on 2016-10-07 06:34:33

Riemann Zeta Function and Relationship to Prime Numbers

Authors: Ricardo Gil
Comments: 2 Pages.

ζ(s)=1/(((1/(2))/log(2)))+ 1/(((1/(3))/log(3)))+ 1/(((1/(4))/log(4)))+1/(((1/(5))/log(5))) is a form of Riemann Zeta Function and it shows an approximate relationship between the Riemann Zeta Function and Prime Numbers.
Category: Number Theory

[9] viXra:1610.0082 [pdf] submitted on 2016-10-07 06:37:51

Nth Prime Equation

Authors: Ricardo Gil
Comments: 1 Page.

The classical Distribution of Primes Equation can be modified to make an Nth Prime Equation which generates the Nth Prime.
Category: Number Theory

[8] viXra:1610.0065 [pdf] replaced on 2016-10-10 23:28:04

Lauricella Hypergeometric Series Over Finite Fields

Authors: Bing He
Comments: 22 Pages.

In this paper we give a finite field analogue of the Lauricella hypergeometric series and obtain some transformation and reduction formulae and several generating functions for the Lauricella hypergeometric series over finite fields. Some of these generalize some known results of Li \emph{et al} as well as several other well-known results.
Category: Number Theory

[7] viXra:1610.0034 [pdf] submitted on 2016-10-03 19:56:15

In 1991 Fermat Last Theorem Has Been Proved (1)

Authors: Chunxuan Jiang
Comments: 6 Pages.

using complex hyperbolic function we prove Fermat last theorem
Category: Number Theory

[6] viXra:1610.0033 [pdf] submitted on 2016-10-03 20:01:14

In 1991 Fermat Last Theorem Has Been Proved (Ii)

Authors: Chunxuan Jiang
Comments: 5 Pages.

using trogonometric function we prove Fermat last theorem
Category: Number Theory

[5] viXra:1610.0024 [pdf] submitted on 2016-10-03 09:06:13

Proving Riemann with Gamma or Euler–Mascheroni Constant (0.5772156649015328606065120900824024310421593359399)

Authors: Ricardo Gil
Comments: 2 Pages.

(1/2 Part)>1.002 (1.002, 2.16, 4.008 & 6.012) Generate Riemann Non Trivial Zero’s Off Of Critical Line. A Riemann Non Trivial Zero off the Critical Line occurs between 1 /2 or .50 and Gamma 0.577215664901532860606512090 08240243104 215 93 359399.When (1/2 Part) = (1.002 , 2.16, 4.008 & 6.012) Riemann Non Trivial Zero’s Are Off .001 To The Rt. Of The Critical Line & When (1/2 Part)= (1 / 2) A Riemann Non Trivial Zero’s Will Be On Critical Line.
Category: Number Theory

[4] viXra:1610.0016 [pdf] replaced on 2016-10-26 05:46:31

A Survey of Rational Diophantine Sextuples of Low Height

Authors: Philip Gibbs
Comments: Pages. DOI: 10.13140/RG.2.2.29253.65761

A rational Diophantine m-tuple is a set of m distinct positive rational numbers such that the product of any two is one less than a rational number squared. A computational search has been used to find over 1000 examples of rational Diophantine sextuples of low height which are then analysed in terms of algebraic relationships between entries. Three examples of near-septuples are found where a rational Diophantine quintuple can be extended to sextuples in two different ways so that the combination fails to be a rational Diophantine septuple only in one pair.
Category: Number Theory

[3] viXra:1610.0009 [pdf] submitted on 2016-10-01 19:37:45

Intrinsic Relations Between Prime Numbers a Prime Number and the Generation of the Prime Twins

Authors: Liujingru
Comments: 4 Pages.

This work reveals the intrinsic relationship of numbers with the conception of “prime multiple” to prove the “hypothesis of twin primes”. Based on this proof, “Goldbach conjecture” is proved with the “Odd-Gaussian Corresponding”. The nature of “prime number” can be thus obtained.Paper is using the axiom Ⅶ twice. For the first time: high high more than nonsingular group, according to the axiom Ⅶ get there will be a (high + high group). Second: high + high group) will be (prime number + prime)
Category: Number Theory

[2] viXra:1610.0008 [pdf] submitted on 2016-10-01 20:19:40

数的内在关系浅论 素数及孪生素数的生成

Authors: 刘静儒
Comments: 4 Pages.

通过“素数的倍数”这一概念,揭示了数的内在关系,论证了“孪生素数猜想”,并在此基础上给出了“奇高组”的定义,并结合“高斯对应”,论文只是两次运用公理Ⅶ。第一次:奇高组多于非奇高组,根据公理Ⅶ得到必有这样的结果:(奇高组+奇高组)。第二次:(奇高组+奇高组)必有这样的结果:(素数+素数),这就证明了“哥德巴赫猜想”。
Category: Number Theory

[1] viXra:1610.0001 [pdf] submitted on 2016-10-01 01:46:45

Proving Grimm’s Conjecture by Stepwise Forming Consecutive Composite Numbers’ Points at the Number Axis

Authors: Zhang Tianshu
Comments: 13 Pages.

Let us consider positive integers which have a common prime factor as a kind, then the positive half line of the number axis consists of infinite many recurring line segments of same permutations of c kinds of integers’ points, where c≥1. In this article we proved Grimm’s conjecture by stepwise change symbols of each kind of composite numbers’ points at the number axis, so as to form consecutive composite numbers’ points under the qualification of proven Legendre-Zhang conjecture as the true.
Category: Number Theory