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[24] viXra:2304.0226 [pdf] submitted on 2023-04-29 07:41:41
Authors: Yuji Masuda
Comments: 1 Page.
Each number has its own meaning. In this chapter, I was able to make explicit the relationship between the meaning of numbers and Ohm's law.
Category: Number Theory
[23] viXra:2304.0222 [pdf] submitted on 2023-04-28 23:47:35
Authors: Theophilus Agama
Comments: 6 Pages.
In this paper, we prove the special squeeze principle for all sufficiently large $nin 2mathbb{N}$. This provides an alternative proof for the asymptotic version of the binary Goldbach conjecture in cite{agama2022asymptotic}.
Category: Number Theory
[22] viXra:2304.0218 [pdf] submitted on 2023-04-27 22:08:49
Authors: Budee U. Zaman
Comments: 12 Pages.
This paper introduces a novel approach to estimating the distribu- tion of prime numbers by leveraging insights from partition theory, prime number gaps, and the angles of triangles. Application of this methodology to infinite sums and nth terms, and propose several ways of defining the nth term of a prime number. By using the Ramanujan infinite series of natural numbers, I am able to derive an infinite series of prime numbers value . Overall, this work represents a significant contribution to the field of prime number theory and sheds new light on the relationship between prime numbers and other mathematical concepts.
Category: Number Theory
[21] viXra:2304.0192 [pdf] submitted on 2023-04-24 07:12:55
Authors: Timothy W. Jones
Comments: 6 Pages.
The quest for an irrationality of pi proof that can be incorporated into an analysis (or a calculus) course is still extant. Ideally a proof would be well motivated and use in an interesting way the topics of such a course. In particular $e^{pi i}$ should be used and the more easily algebraic of derivatives and integrals -- i.e. derivatives. A further worthy goal is to use techniques that anticipate those needed for other irrationality and, maybe even, transcendence proofs. We claim to have found a candidate proof.
Category: Number Theory
[20] viXra:2304.0183 [pdf] submitted on 2023-04-23 02:02:21
Authors: Edoardo Gueglio
Comments: 5 Pages.
This is an example of how with a mathematical software you can make a mathematicalconjecture and help to prove it.
Category: Number Theory
[19] viXra:2304.0182 [pdf] replaced on 2023-10-13 23:33:37
Authors: Tsuneaki Takahashi
Comments: 4 Pages.
Investigation is tried about approach to Collatz conjecture and its integer space.
Category: Number Theory
[18] viXra:2304.0181 [pdf] replaced on 2023-08-26 14:27:36
Authors: Ihsan Raja Muda Nasution
Comments: 4 Pages.
The prime numbers have very irregular pattern. The problem of finding pattern in the prime numbers is the long-standing open problem in mathematics. In this paper, we try to solve the problem axiomatically. And we propose some natural properties of prime numbers.
Category: Number Theory
[17] viXra:2304.0166 [pdf] submitted on 2023-04-20 23:55:17
Authors: Kuiying Yan
Comments: 15 Pages.
Yitang Zhang proved in 2013 that there are infinitely many pairs of prime numbers differing by 70 million, it has been proved now that there are infinitely many pairs of prime numbers differing by 246. In this paper, we use the sievemethod invented by Snndaram in 1934 to find out the solution of triple prime numbers and twin prime numbers, and find the general solution formula of the subset, i.e, an1 + b which is result of each subset, such as 3n + 1, 5n + 2, 7n + 3, 9n + 4, 11n+ 5, 13n+ 6, 15n+ 7, 17n+ 8, · · · in 2mn+n+m, modulo x respectively (x ≤ 3 takes prime). This general solution formula is used to prove the triple prime conjecture and the twin prime conjecture.
Category: Number Theory
[16] viXra:2304.0123 [pdf] submitted on 2023-04-18 00:38:35
Authors: John Evans Bwire
Comments: 14 Pages.
The main purpose of this paper is based on the general idea that an equation of this form can’t be a^x+b^x=c algebraically. In this question, the derived formula ((βw-convergence) with mathematical proof can be used to solve such an equation with ease. Since the formula is purely invented with my own approach, the article lacks references.
Category: Number Theory
[15] viXra:2304.0122 [pdf] replaced on 2026-02-03 21:10:11
Authors: Kurmet Sultan
Comments: 3 Pages.
It was proved that for a factorial to be a solution to Brocard's problem, it must be representable as a product of two natural numbers differing by 2. It was then proved that only factorials, which are known solutions to Brocard's problem, can be represented as a product of two natural numbers differing by 2. It follows from this that Brocard's Diophantine equation n!=t^2-1 has no solutions other than the classical one (n,t) = (4,5), (5,11), (7,71).
Category: Number Theory
[14] viXra:2304.0115 [pdf] submitted on 2023-04-16 13:03:07
Authors: Edgar Valdebenito
Comments: 5 Pages.
The Erdös-Borwein constant is the sum of the reciprocals of the Mersenne numbers. It is named after Paul Erdös and Peter Borwein.
Category: Number Theory
[13] viXra:2304.0113 [pdf] replaced on 2023-07-25 20:54:31
Authors: Oussama Basta
Comments: 4 Pages. A better version
The Goldbach’s Conjecture is an astonishing proposition that stands as one of the most renowned and enduring unsolved problems in number theory and mathematics. This research aims to provide a proof for this remarkable conjecture. The approach to be followed for the proof is yielded by using a predefined system of equations, and with a relatively simple analysis. The proof is quite simple compared to the size of the problem. In the second part of this study, we leverage the same system of equations to develop a general mathematical framework for predicting prime numbers within the known sequence, laying down a general mathematical framework that is computationally concise and can just achieve the objective. With proper selection of the coefficients of the equations in the algorithm, it’s guaranteed that prime numbers are among the outputs. The algorithm consists of basic arithmetic operations which is by itself ground breaking. The proof of the algorithm is also astoundingly straightforward and compact.
Category: Number Theory
[12] viXra:2304.0071 [pdf] submitted on 2023-04-11 03:11:11
Authors: Dominique Fosse
Comments: 8 Pages.
Given three generators A, B, C of GL2(Z), we propose an explicit formula of decomposition of any element in $langle A,B,Cangle$.
Category: Number Theory
[11] viXra:2304.0056 [pdf] submitted on 2023-04-08 02:20:32
Authors: Giovanni Di Savino
Comments: 4 Pages.
Perfect numbers were defined by Euclid with a proposition: "If we want as many numbers as we want starting from a unit, they are continuously arranged in double proportion, until the sum of all becomes a prime, and if the sum multiplied in the last one forms a , the product will be perfect"; Euler proved that even perfect numbers can be generated as defined by Euclid and are the result of (2^n -1) * 2^(n-1). Odd perfect numbers can be defined and generated with the proposition and algorithm with which even perfect numbers are defined and generated with the following modifications: a) the prime number 2 reported in Euler's algorithm is replaced by one of the infinite numbers first courses ≥ 3; b) the distance that the prime number must have from the result of a power of prime numbers ≥ 3^n is 2; c) with prime numbers ≥ 3, the "double proportion", reported in Euclid's proposition and generated by the number 2, becomes the triple proportion or the quintuple or.......the proportion of the nth prime number. With the modifications to situations defined as similar, "the generation of perfect odds is similar to the generation of perfect evens" and, also the algorithms with which the perfect numbers are generated are similar: the even perfect numbers are the result of ((2^n -1) * 2^(n-1))/(2-1), the odd perfect numbers are the result of ((prime ≥ 3^n -2) * prime ≥ 3^(n-1))/( first≥3-1).
Category: Number Theory
[10] viXra:2304.0050 [pdf] submitted on 2023-04-08 03:24:25
Authors: John Robert Eaton
Comments: 19 Pages.
Within my paper I begin by defining some important termi- nology. Then I generalize the Collatz Conjecture to a wider class of problems, which I leverage to provide a path to a non-constructive proof of the Collatz Conjecture. Ulitmately, I did not succeed in proving the Collatz Conjecture; however, I believe I have made the problem tractable. The problem I reduced the Collatz Conjecture to is beyond my capabilities. After working through my non-constructive results, I provide some constructive results concerning the collatz conjecture. For example, 2957851400532535270158974145876 converges to one. I conclude with closing remarks.
Category: Number Theory
[9] viXra:2304.0049 [pdf] submitted on 2023-04-07 00:45:28
Authors: Baoqi He, Yong Zhao
Comments: 3 Pages.
In this paper, we introduce Goldbach Conjecture and Twin Prime Conjecture: history, development, public dissemination in China, and propose doubt about the effectiveness of Analytical Number Theory
Category: Number Theory
[8] viXra:2304.0041 [pdf] submitted on 2023-04-05 02:05:50
Authors: Russell Leidich
Comments: 13 Pages.
Any prospective proof of the infamous Riemann hypothesis might be facilitated to someextent by the discovery of an infinite series bearing all of the nontrivial roots of the Riemannzeta function ζ(z), that is, those which exist on the critical strip -- and no others. Absent such aseries, our goal here is to make progress in that direction.
Category: Number Theory
[7] viXra:2304.0034 [pdf] submitted on 2023-04-05 00:38:21
Authors: Huhnkie Lee
Comments: 12 Pages.
This paper is designed to clarify points made in our previous paper, "A Probabilistic Proof of Goldbach's Conjecture". We also present a proof of ‘twin prime conjecture’. We also examine some other aspects that relate to prime number distribution.
Category: Number Theory
[6] viXra:2304.0029 [pdf] replaced on 2023-07-25 02:43:00
Authors: Ahmed Idrissi Bouyahyaoui
Comments: 3 pages in English and 3 pages in French.
Let xi = 2^αi*yi and vi = 2^βi*zi , x0, yi and zi are odd integers.The sequence {xi + vi} built by Collatz algorithm is a Collatz sequence if it exists n such that xn + vn = 1.By hypothesis S(y0) is a Collatz sequence, then it exists at least one i such that yi = 1, xi = 2^αi*yi = 2^αi and vi = zi (because vi < xi and xi + vi > 0).As for every k ≥ i yk Є [1, 4, 2], xk + vk is of form : xk + vk = 2^αk + zk.For every optimal point (k, xk + vk), continuous and differentiable function f(α) = x + v = 2^α + z has a zero derivative and the primitive function z = - 2^α + c, c is an arbitrary integer constant.For every optimum we have : f(α) = c.At the optimum minimum = 1, it exists at least one n such that, yn Є [1, 4, 2], f(αn) = xn + vn = 2^αn + zn = 2^αn - 2^αn + c = c. For the minimum f(αn) = 1, it suffices to set c = 1 and so we have : f(αn) = xn + vn = 1, xn = 2^αn and vn = — (2^αn — 1).Conclusion :The sequence S(x0 +2) ends in 1 and has the only cycle [1, 4, 2, 1].So by recurrence, every positive integer number gives a Collatz sequence.
Category: Number Theory
[5] viXra:2304.0022 [pdf] submitted on 2023-04-03 23:59:05
Authors: Gaurav Krishna
Comments: 27 Pages.
We consider n to have only odd values, and even values are written in the form; n.2^b. We create a predefined function r_b(n).Create an identical function to Collatz transformations, we use the properties of said function to probe if some number n can explode to infinity. We study n_x in detail, establish pattern for n_x modulo 3. We use our understanding to probe if some number n, can loop to itself with more than one transformation.
Category: Number Theory
[4] viXra:2304.0017 [pdf] replaced on 2023-05-25 08:34:37
Authors: Óscar E. Chamizo Sánchez
Comments: 3 Pages.
In this paper we present the concept of mirror composite numbers. Mirror composite numbers are composite numbers of the form 2n-p for somen positive natural number and p prime. We shall show that the factorization of these numbers have interesting properties in order to face the Goldbachconjecture by the divide et impera method.
Category: Number Theory
[3] viXra:2304.0010 [pdf] submitted on 2023-04-01 22:15:02
Authors: Kurmet Sultan
Comments: 5 Pages. (Name added to Article by viXra Admin as required)
The article describes the relationship between the power of natural numbers and the factorial, established as a result of applying the binomial transformation method to the sequence of the of natural numbers.
Category: Number Theory
[2] viXra:2304.0007 [pdf] submitted on 2023-04-01 22:24:03
Authors: Poliagapitos
Comments: 9 Pages. (Abstract added by viXra Admin; first name is required - Please conform!)
Transcendental numbers expressed by infinite continued fractions.
Category: Number Theory
[1] viXra:2304.0001 [pdf] submitted on 2023-04-01 21:17:39
Authors: Rudi Mayers
Comments: 12 Pages. I am no longer affiliated to an Academic Institution and having devised this proof last September it has been challenging to publish the work. I currently work in Industry.
It is well known to mathematicians, that there is an infinite number of primes as proven via simple logic by Euclid in the 4th Century BC1,2 and confirmed by Leonhard Euler in 17373. In 1846 French mathematician Alphonse de Polignac4 proposed that any even number can be expressed in infinite ways as the difference between two consecutive primes, since when or perhaps possibly even before that all the way back to Euclid, mathematicians have been trying to prove that there is an infinite number of TWIN PRIMES. In this paper a relatively simple proof is presented, that there is indeed an infinity of TWIN PRIMES based on a new approach without any assumptions.
Category: Number Theory
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