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