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[15] viXra:2101.0176 [pdf] replaced on 2021-02-22 02:48:42
Authors: Toshihiko Ishiwata
Comments: 23 Pages.
This paper is a trial to prove Riemann hypothesis which says “All non-trivial zero points of Riemann zeta function ζ(s) exist on the line of Re(s)=1/2.” according to the following process. 1 We have the infinite series A and B from the equation that gives ζ(s) analytic continuation to Re(s)＞0 and the two formulas (1/2+a+bi, 1/2-a-bi) that show non-trivial zero point of ζ(s). The sum of A must be equal to the sum of B. 2 We divide both A and B into the infinite groups after changing terms order of both A and B. 3 We find that the sum of A can be equal to the sum of B if only a=0 by comparing the infinite groups made from A with those from B. Therefore zero point of ζ(s) must be 1/2±bi due to a=0 and other zero point does not exist.
Category: Number Theory
[14] viXra:2101.0174 [pdf] replaced on 2021-04-25 03:57:35
Authors: Kurmet Sultan
Comments: 3 Pages. This is the Russian version of the manuscript.
The article contains extended versions of Fermat's little theorem and Euler's theorem, as well as a theorem intended for any remainder, which generalizes Fermat's and Euler's theorems.
Category: Number Theory
[13] viXra:2101.0171 [pdf] replaced on 2021-03-20 10:38:19
Authors: Berndt Gensel, Theophilus Agama
Comments: 6 Pages. The proof of the main lemma is under construction.
In this paper we use a new method to study problems in the additive number theory (see \cite{CoP}). With the notion of circle of partition as a set of points whose weights are natural numbers of a particular subset under an additive condition we are almost able to prove the binary Goldbach conjecture.
Category: Number Theory
[12] viXra:2101.0164 [pdf] submitted on 2021-01-25 22:13:07
Authors: Tai-Choon Yoon
Comments: 7 Pages.
There are four paradoxical summations of the infinite series, $1-2+3-4+\cdots=\frac{1}{4}$ as even Leonhard Euler admitted this infinite series, the Ramanujan summation $1+2+3+4+\cdots=-\frac{1}{12}$ which is widely cited, especially in Riemann zeta function as if it were correct, Grandi's series $1-1+1-1+\cdots=\frac{1}{2}$, and $1+1+1+1+\cdots=-\frac{1}{2}$. These infinite series are inconsistent.
Category: Number Theory
[11] viXra:2101.0156 [pdf] submitted on 2021-01-24 19:32:04
Authors: Luke Townend
Comments: 3 Pages.
How to visualize divide by a bigger number using modular arithmetic and the Pronic numbers.
Category: Number Theory
[10] viXra:2101.0155 [pdf] submitted on 2021-01-25 20:00:25
Authors: Yves De-Mervent, Sarra Neji
Comments: 73 Pages. en français. © SGDL n° 2013-07-0220. © ISBN 978-2-919648-32-0 disponible aux Éditions Pontcerq.
La théorie des nombres repose sur plusieurs conventions. Nous reprenons la notion d’entiers naturels afin de montrer la pertinence de la remise en question de ces conventions, permettant d’apporter de nouveaux résultats. Nous démontrons des événements similaires entre les nombres premiers et les nombres composés d’un côté, et entre les couples de nombres premiers jumeaux et les couples de nombres composés jumeaux d’un autre côté. Nous démontrons une analogie entre les nombres entiers naturels et les rhésus sanguins du systèmes ABO.
Number theory is based on several conventions. We study the concept of natural numbers to show the relevance of questioning these conventions, enabling it to bring new results. We demonstrate similar events between prime numbers and composite numbers on the one hand, and between pairs of twin primes and pairs of twin composite numbers on the other hand. We demonstrate an analogy between natural numbers and the Rh blood groups of the ABO system.
Category: Number Theory
[9] viXra:2101.0133 [pdf] submitted on 2021-01-21 14:52:06
Authors: Babacar Gueye
Comments: 8 Pages. [Corrections made by viXra Admin to conform with the requirements on the Submission Form]
Consider k runners on a circular track of unit length. At t=0, all the runners are at the same position and start to run; the runners speeds are distincts. A runner is said to be lonely at time t, if he is at a distance of at least 1/k from every other. The lonely runner conjecture states that each runner is lonely at some times. It is said we not lost generality to assume that the runners have integer speeds. It is knew that the conjecture is proved until seven runners at 2008. Then consider here integer speeds and prove the conjecture in general.
Category: Number Theory
[8] viXra:2101.0125 [pdf] submitted on 2021-01-20 12:17:25
Authors: Juan Elias Millas Vera
Comments: 2 Pages.
With the use of my own descriptions of the sets and subsets of numbers I could do a simple but effective proof of this conjecture.
Category: Number Theory
[7] viXra:2101.0117 [pdf] submitted on 2021-01-19 00:52:50
Authors: Takamasa Noguchi
Comments: 4 Pages.
I created an approximate calculation formula for the zeta function and the L function. The range is 1
Category: Number Theory
[6] viXra:2101.0108 [pdf] submitted on 2021-01-17 13:07:09
Authors: Méhdi Pascal
Comments: 38 Pages. [Corrections are made by viXra Admin to comply with the rules of viXra.org]
Bernoulli's number theory plays a very important role in all mathematics, we find them in number theory, arithmetic, analysis, and even topology. The aim of this paper is to give the proofs to the most fundamental theorems of these numbers, such as the Von Staudt-Clausen theorem, Adams' theorem, Kummer's congruence, Voronoï congruence, Ramanujan recurrences, and many other new formulas.
Category: Number Theory
[5] viXra:2101.0107 [pdf] submitted on 2021-01-17 13:15:48
Authors: Babacar Gueye
Comments: 4 Pages. [Corrections made by viXra Admin to conform with the requirements on the Submission Form]
In mathematics, the Riemann Hypothesis is a conjecture gived in 1859 by the deutch mathematician Bernard Riemann. It says that the non trivial zero of the zeta fonction of Riemann have all for real part $\frac{1}{2}$. We give here a proof of this conjecture that uses his relation with the Dirichlet fonction etz on the part of the plan $\R(s)$, where $s$ is a complex number. We use exactly the fact that if $\zeta(s) = 0$ then $\zeta(1 - s) = 0$, and better if $\zeta(s) = \zeta(1 - s)$ then $\R(s) =\frac{1}{2}$
Category: Number Theory
[4] viXra:2101.0079 [pdf] replaced on 2021-02-08 01:45:04
Authors: Junya Sebata
Comments: 10 Pages. JP J. Algebra, Number Theory Appl. 51(1) (2021), 55 - 75.
This paper gives the simple and necessary condition of Fermat Wiles Theorem with mainly providing one method to analyze natural numbers and the formula X^n + Y^n = Z^n logically and geometrically, which is positioned in combinatorial design theory. The condition is gcd(X, E)^n = X − E ∧ gcd(Y, E)^n = Y − E in ¬(n | XY ), or gcd(X, E)^n/n = X − E ∧ gcd(Y, E)^n = Y − E in n | X ∧ ¬(n | Y ). Provided that E denotes E = X + Y − Z, n is a prime number equal to or more than 2, and X, Y, Z are coprime numbers.
Category: Number Theory
[3] viXra:2101.0072 [pdf] submitted on 2021-01-11 07:22:50
Authors: Yuji Masuda
Comments: 3 Pages.
First, ±∞ is constant at any observation point (position). If a set of real numbers is R, then On the other hand, when x (∈R)is taken on a number line, the absolute value X becomes larger toward ± ∞ as the absolute value X is expanded. Similarly, as the size decreases, the absolute value X decreases toward 0. Furthermore, x (-1) represents the reversal of the direction of the axis. Second, from the definition of napier number e.
Category: Number Theory
[2] viXra:2101.0044 [pdf] submitted on 2021-01-07 11:18:45
Authors: Stephen M Marshall
Comments: 33 Pages.
The author Stephen Marshall, through research, recently discovered six new Mathematical Conjectures, they can be stated simply, but surprisingly are very easy to prove. This is unusual for most Number Theory Conjectures, usually they are very difficult to prove. The author also provides the proof for each of the six conjectures.
Category: Number Theory
[1] viXra:2101.0014 [pdf] submitted on 2021-01-03 18:07:52
Authors: Juan Moreno Borrallo
Comments: 8 Pages.
In this brief paper it is proved the inexistence of odd perfect numbers using elementary methods. From the definition of a perfect number P, and operating with the set of proper divisors less than the square root of P, the existence of some odd perfect number is linked to the existence of solution of a particular egyptian fraction with an special restriction. Proving that such an egyptian fraction with that restriction can not exist, it is concluded that no odd perfect number does exist.
Category: Number Theory
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