Number Theory

1910 Submissions

[45] viXra:1910.0654 [pdf] replaced on 2019-11-02 04:55:39

Goldbach's Conjecture

Authors: Yuji Masuda
Comments: 1 Page.

This is a proof of Goldbach's conjecture.
Category: Number Theory

[44] viXra:1910.0650 [pdf] replaced on 2019-11-02 04:39:55

Proof(Definition⑪)

Authors: Yuji Masuda
Comments: 1 Page.

This is proof of a famous formula.
Category: Number Theory

[43] viXra:1910.0636 [pdf] submitted on 2019-10-30 22:53:32

On Prime Numbers⑯(DefinitionⅩ)

Authors: Yuji Masuda
Comments: 1 Page.

This is collaboration3.
Category: Number Theory

[42] viXra:1910.0634 [pdf] submitted on 2019-10-30 00:30:29

On Prime NUMBERS⑮❨DefinitionⅨ❩

Authors: Yuji Masuda
Comments: 1 Page.

This is collaboration２.
Category: Number Theory

[41] viXra:1910.0565 [pdf] replaced on 2019-10-28 19:05:17

On Prime Numbers⑭(DefinitionⅧ)

Authors: Yuji Masuda
Comments: 1 Page.

This is collaboration.
Category: Number Theory

[40] viXra:1910.0563 [pdf] submitted on 2019-10-27 02:56:14

A^x + B^y = C^z Part 1: my Theorem

Authors: Quang Nguyen Van
Comments: 3 Pages.

Adding to the known partial results, two famous Math problems : Beal conjecture and Fermat - Catalan conjecture are proved by one theorem -QS theorem that we propose in this article, and also means that the elementary proof of FLt has been found.
Category: Number Theory

[39] viXra:1910.0558 [pdf] submitted on 2019-10-27 07:27:30

Division by Zero Fallacies Using Transmathematics

Authors: William F. Gilreath
Comments: 10 Pages. Published in the General Science Journal

Three fallacies that illustrate why division by zero is frequently considered undefined operation are examined. The example fallacies consider the unique case of zero divided by zero. Two examples are fallacies of equality, and the other is an example of ambiguity in the solution for an equation. These fallacies are examined using the transmathematic number nullity F. By utilizing nullity, division by zero is no longer an undefined or indeterminate operation, but a consistent, well-defined operation in arithmetic.
Category: Number Theory

[38] viXra:1910.0551 [pdf] replaced on 2019-10-30 02:26:02

Using Decimals to Prove Zeta(n >= 2) is Irrational

Authors: Timothy W. Jones
Comments: 4 Pages. A few corrections and improvements per some suggestions received.

With a strange and ironic twist an open number theory problem, show Zeta(n) is irrational for natural numbers greater than or equal to 2, is solved with the easiest of number theory concepts: the rules of representing fractions with decimals.
Category: Number Theory

[37] viXra:1910.0549 [pdf] submitted on 2019-10-26 17:08:03

On the Possible Mathematical Connections Between Some Equations of Various Topics Concerning the Dilaton Value, the D-Brane, the Bouncing Cosmology and Some Sectors of Number Theory (Ramanujan Riemann’s Functions and Rogers-Ramanujan Continued Fractions)

Authors: Michele Nardelli, Antonio Nardelli
Comments: 108 Pages.

In this research thesis, we have described some new mathematical connections between some equations of various topics concerning the Dilaton value, the D-Brane, the Bouncing Cosmology and some sectors of Number Theory (Riemann’s functions of S. Ramanujan and Rogers-Ramanujan continued fractions).
Category: Number Theory

[36] viXra:1910.0538 [pdf] submitted on 2019-10-26 07:33:48

On Prime Numbers⑬

Authors: Yuji Masuda
Comments: 1 Page.

This is Primes⑬
Category: Number Theory

[35] viXra:1910.0499 [pdf] replaced on 2019-10-24 02:25:43

On Prime Numbers⑫

Authors: Yuji Masuda
Comments: 1 Page.

This is Primes⑫
Category: Number Theory

[34] viXra:1910.0494 [pdf] submitted on 2019-10-24 05:10:18

The Proof of Goldbach’s Conjecture

Authors: Zhiping Dai
Comments: 7 Pages.

Since the set of AS(+) and AS(×) is a bijective function, we use the improved the theorem of asymptotic density to prove that there exist prodcut of two odd primes in any AS(×). At the same time, in any AS(+), the sum of two odd primes can be obtained.
Category: Number Theory

[33] viXra:1910.0475 [pdf] submitted on 2019-10-23 21:44:14

A Circle Driven Proof of the Twin Prime Conjecture

Authors: Derek Tucker
Comments: 1 Page. Replaces the previous submission

Twin prime conjecture is proven from the observation that all composite odd numbers with factors greater than three occur in the cycle (0pm, 1pm, 5pm, 6pm), This draws circles with diameter 2p_m^2, and inter circle interval of 4p_m^2. For exclusively composite numbers we have |p_m^2±6p_m |.
Category: Number Theory

[32] viXra:1910.0444 [pdf] submitted on 2019-10-23 12:21:40

On Some New Possible Mathematical Connections Between Some Equations of the Ramanujan’s Manuscripts, the Rogers-Ramanujan Continued Fractions and Some Sectors of Particle Physics, String Theory and D-Branes

Authors: Michele Nardelli, Antonio Nardelli
Comments: 152 Pages.

In this research thesis, we have described some new mathematical connections between some equations of the Ramanujan’s manuscripts, the Rogers-Ramanujan continued fractions and some sectors of Particle Physics (physical parameters of mesons and dilatons, in particular the values of the masses), String Theory and D-branes.
Category: Number Theory

[31] viXra:1910.0411 [pdf] submitted on 2019-10-21 03:47:35

On Prime NumbersⅪ

Authors: Yuji Masuda
Comments: 1 Page.

This is primes⑪
Category: Number Theory

[30] viXra:1910.0395 [pdf] submitted on 2019-10-21 11:38:49

Anti-gravity Inverse Yeet Theorem

Authors: Siddharth Bhatt
Comments: 1 Page.

When working with fractions, gravity always acts towards the division bar. This leads to a very non-intuitive result when yeeting a coefficient into the index. Since inverse yeeting is now done along the direction of gravity, the number itself gets inverted after reaching the index.
Category: Number Theory

[29] viXra:1910.0367 [pdf] submitted on 2019-10-20 11:45:58

Prime Intra Squares Conjecture

Authors: Derek Tucker
Comments: 3 Pages.

Proof of Legendre's conjecture by elementary means.
Category: Number Theory

[28] viXra:1910.0366 [pdf] replaced on 2024-11-29 10:26:41

A Complete Proof of Beal's Conjecture Final Version

Authors: Abdelmajid Ben Hadj Salem
Comments: 58 Pages. It is the final version of my proof of Beal's conjecture. Submitted to the journal Mathematika. Comments welcome.

In 1997, Andrew Beal announced the following conjecture: Let A, B, C, m, n, and l bepositive integers with m, n, l > 2. If A^m + B^n = C^l then A, B, and C have a commonfactor. We begin to construct the polynomial P(x) = (x − A^m)(x − B^n)(x + C^l) =x^3 − px + q with p, q integers depending on A^m, B^n and C^l. We resolve x^3 − px + q = 0and we obtain the three roots x_1, x_2, x_3 as functions of p and a parameter θ. SinceA^m, B^n, −C^l are the only roots of x^3 − px + q = 0, we discuss the conditions thatx_1, x_2, x_3 are integers and have or do have not a common factor. Three numericalexamples are given.
Category: Number Theory

[27] viXra:1910.0365 [pdf] submitted on 2019-10-20 11:57:05

Polynomial Time Factoring Method

Authors: Derek Tucker
Comments: 1 Page.

Let y = exp(ln # - ln x) mod 1. The results show y = 0 for integer x if and only if x is a factor of #.
Category: Number Theory

[26] viXra:1910.0364 [pdf] submitted on 2019-10-19 15:17:19

On the Possible Mathematical Connections Between Some Equations of Various Sectors Concerning the D-Branes and Some Ramanujan’s Modular Equations and Approximations to π.

Authors: Michele Nardelli, Antonio Nardelli
Comments: 59 Pages.

In this research thesis, we have described some new mathematical connections between some equations of various sectors concerning the D-Branes and some Ramanujan’s modular equations and approximations to π.
Category: Number Theory

[25] viXra:1910.0349 [pdf] replaced on 2019-11-04 03:39:57

Periodic Sequences of Progressions of the Same Type

Authors: Y.Mieno
Comments: 5 Pages.

A few progressions of the same type and their periodic sequences.
Category: Number Theory

[24] viXra:1910.0322 [pdf] submitted on 2019-10-18 12:33:20

On the Possible Mathematical Connections Between Some Equations of Various Topics Concerning the D-Branes and Some Sectors of Number Theory (Rogers-Ramanujan Continued Fractions and Mock Theta Functions).

Authors: Michele Nardelli, Antonio Nardelli
Comments: 201 Pages.

In this research thesis, we have described some new mathematical connections between some equations of various topics concerning the D-Branes and some sectors of Number Theory (Rogers-Ramanujan continued fractions and mock theta functions).
Category: Number Theory

[23] viXra:1910.0317 [pdf] submitted on 2019-10-17 02:18:31

吴叶唐寅：theorem（四）Odd Number（2N＋1=2＋Pa、or、2N＋1=2×Pa＋Pb）

Authors: Wu Ye TangYin
Comments: 13 Pages. Please forgive me for my low level of mathematics writing. The article is right

According to the random theory and hypothesis theory, the calculation of any number is pushed to infinity. In this paper, 2n-a = 2 * B (B does not know whether it is prime number, or compound number. So the hypothesis plays an important role in judgment. If B is equal to prime, then there is no need to calculate. If B is a compound number, its factorization prime factor, we can get the prime number, and then we can calculate it. But infinity belongs to the unknown. We don't know what it is to decompose prime factors. Only a, B, C, D.. Then suppose it is a composite number. In this paper, it is only for infinite odd numbers. Is there an inverse column? Odd numbers are not equal to two same prime numbers, plus the sum of odd prime numbers.)
Category: Number Theory

[22] viXra:1910.0316 [pdf] submitted on 2019-10-17 02:46:52

吴叶唐寅：theorem（三）Arbitrary Even Numbers(2n = pa ＋ Pb )

Authors: Wu Ye TangYin
Comments: 13 Pages. Who is willing to help me revise the article? My writing level is low. But theoretical logic is right. Help me get in touch with math magazines.

o prove the idea, assuming that any even number can not be equal to the sum of two prime numbers, then according to the analog computing logic. Subject: Use hypothesis to judge unknown. In infinite even numbers, there are only numbers, a, b, c, D. Can only be judged; it's prime, or compound. When: 2N－P=B (B, it is a prime number, or it is a compound number), the hypothesis is used as the basis of judgment. If B equals a prime number, there is no need to calculate it. But B is an unknown number. Judge it to be a prime or a compound number. Assuming a complex number, it can decompose the prime factor. We can get prime numbers. Here, we use hypothesis computing theory to push the unknown to infinity.。Find any even number, there are prime pairs.（Abbreviation：2N=Pa＋Pb）
Category: Number Theory

[21] viXra:1910.0281 [pdf] replaced on 2019-12-29 20:29:20

A New Look at Potential vs. Actual Infinity

Authors: Felix M. Lev
Comments: 11 Pages.

The {\it technique} of classical mathematics involves only potential infinity, i.e. infinity is understood only as a limit, and, as a rule, legitimacy of every limit is thoroughly investigated. However, {\it the basis} of classical mathematics does involve actual infinity: the infinite ring of integers $Z$ is the starting point for constructing infinite sets with different cardinalities, and, even in standard textbooks on classical mathematics, it is not even posed a problem whether $Z$ can be treated as a limit of finite sets. On the other hand, finite mathematics starts from the ring $R_p=(0,1,...p-1)$ (where all operations are modulo $p$) and the theory deals only with a finite number of elements. We give a direct proof that $Z$ can be treated as a limit of $R_p$ when $p\to\infty$, and the proof does not involve actual infinity. Then we explain that, as a consequence, finite mathematics is more fundamental than classical one.
Category: Number Theory

[20] viXra:1910.0261 [pdf] submitted on 2019-10-15 19:05:23

Prime Opinion Part I

Authors: Derek Tucker
Comments: 7 Pages.

Our objective is to demistify prime gaps in the integers. We will show that the explicit range of prime gaps in the integers is bounded from below by two and above by the expression 〖2p〗_(n-1) , valid for gaps beginning 〖(p〗_n^2-1)-p_(n-1). This upper bound theoretically becomes necessarily greater than empirical observation within empirically verified range, enabling explicit closure on prime gap issues. These results confirm the prime pattens conjecture and the Prime Inter-Square Conjecture (PISC) Legendre’s conjecture.
Category: Number Theory

[19] viXra:1910.0239 [pdf] submitted on 2019-10-14 16:47:14

Inequality in the Universe, Imaginary Numbers and a Brief Solution to P=NP? Problem

Authors: Mesut Kavak
Comments: 3 Pages.

While I was working about some basic physical phenomena, I discovered some geometric relations that also interest mathematics. In this work, I applied the rules I have been proven to P=NP? problem over impossibility of perpendicularity in the universe. It also brings out extremely interesting results out like imaginary numbers which are known as real numbers currently. Also it seems that Euclidean Geometry is impossible. The actual geometry is Riemann Geometry and complex numbers are real.
Category: Number Theory

[18] viXra:1910.0237 [pdf] submitted on 2019-10-14 22:04:42

On Prime NumberⅩ

Authors: Yuji Masuda
Comments: 1 Page.

This is on primes⑩
Category: Number Theory

[17] viXra:1910.0201 [pdf] submitted on 2019-10-12 14:31:09

Further Mathematical Connections Between Some Equations of Dirichlet L-Functions, Some Equations of D-Branes and the Rogers-Ramanujan Continued Fractions. III

Authors: Michele Nardelli, Antonio Nardelli
Comments: 113 Pages.

In this research thesis, we have described some new mathematical connections between some equations of Dirichlet L-functions, some equations of D-Branes and Rogers-Ramanujan continued fractions.
Category: Number Theory

[16] viXra:1910.0182 [pdf] submitted on 2019-10-11 22:27:52

On Prime Numbers Ⅸ～Special Edition～

Authors: Yuji Masuda
Comments: 1 Page.

I was suprised.
Category: Number Theory

[15] viXra:1910.0180 [pdf] submitted on 2019-10-11 02:45:25

Factorization of the Numbers of the Form N + N ^ 2

Authors: Pedro Hugo García Peláez
Comments: 4 Pages.

Factorization of the numbers of the form n + n ^ 2 it can be done with a certain algorithm.
Category: Number Theory

[14] viXra:1910.0179 [pdf] submitted on 2019-10-11 02:53:16

Factorización de Los Números Naturales de la Forma N+n^2

Authors: Pedro Hugo García Peláez
Comments: 4 Pages.

Los números de la forma n+n^2 se pueden factorizar con un cierto algoritmo.
Category: Number Theory

[13] viXra:1910.0157 [pdf] submitted on 2019-10-10 07:42:33

On the Possible Mathematical Connections Between Some Equations of Certain Dirichlet Series, Some Equations of D-Branes and Ramanujan Formula that Link π, e and the Golden Ratio. II

Authors: Michele Nardelli, Antonio Nardelli
Comments: 308 Pages.

In this research thesis, we have described some new mathematical connections between some equations of certain Dirichlet series, some equations of D-Branes and Rogers-Ramanujan formulas that link π, e and ϕ.
Category: Number Theory

[12] viXra:1910.0142 [pdf] submitted on 2019-10-09 07:17:22

N-Ésimo Primo. Primer Millón de Números Primos Calculados Con Una Fórmula Para el N-Ésimo Primo

Authors: Horacio useche losada
Comments: 25 Pages. Primer millón de números primos calculados con una fórmula para el n-ésimo primo

Conseguir una fórmula, un procedimiento o algoritmo para computar el n- ésimo primo, ha sido siempre un viejo anhelo de los matemáticos. Sin em- bargo, en la literatura cientı́fica solo se reportan fórmulas basadas en el teo- rema de Wilson, las cuales, carecen de un valor práctico y solo pueden tener un interés estrictamente teórico, ya que no se puede llegar muy lejos al in- tentar su uso en cálculos concretos. Esta investigación retoma un trabajo del profesor Ramón Fandiño,1 el cual, presenta en 1980 una relación funcional a partir de la cual se puede com- putar el n-ésimo primo en función de los n − 1 primos anteriores. Para con- seguir el objetivo, el profesor Fandiño realiza cinco ajustes, tres por mı́nimos cuadrados y dos por técnicas implementadas por él mismo, con lo cual con- sigue calcular los primeros 5000 primos. Siguiendo la lı́nea de investigación del citado profesor, pero haciendo al- gunos cambios importantes en el modelo matemático usado y con un menor número de ajustes, he conseguido computar un millón de números pri- mos, advirtiendo que es posible computar muchos más,2 si se cuenta con las herramientas de hardware adecuadas. En esta ocasión, he usado un PC casero3 , una máquina corriente que logró computar dicha cantidad en tan solo una hora y 21 minutos! Para hacernos una idea del esfuerzo computacional, en su momento el profesor Fandiño utilizó, no un PC, sino un computador de verdad, un IBM 360/44 que era la máquina más poderosa del centro de cómputo de la UN (y posiblemente de Colombia).4 Con un “juguete”de cómputo, me complace presentar esta cifra que se enmarca en una polı́tica denominada “resultados sorprendentes con recursos mediocres”tal y como acontece con otros trabajos de este autor (ver [5], [6], y [7]). Espero muy pronto superar esta cifra usando un hardware más poderoso, naturalmente.
Category: Number Theory

[11] viXra:1910.0137 [pdf] submitted on 2019-10-09 10:09:21

The Collatz Conjecture. Order and Harmony in the Sequence Numbers

Authors: Miguel Cerdá Bennassar
Comments: 35 Pages.

Abstract: I propose a numerical table that demonstrates visually that the sequences formed with Collatz's algorithm always reach 1.
Category: Number Theory

[10] viXra:1910.0129 [pdf] submitted on 2019-10-09 02:07:26

On Prime NumbersⅧ

Authors: Yuji Masuda
Comments: 49 Pages.

This is primes⑧
Category: Number Theory

[9] viXra:1910.0120 [pdf] submitted on 2019-10-08 00:06:45

On Prime NumbersⅦ

Authors: Yuji Masuda
Comments: 23 Pages.

This is on primes⑦
Category: Number Theory

[8] viXra:1910.0117 [pdf] submitted on 2019-10-08 06:37:37

On the Possible Mathematical Connections Between Some Equations of Certain Dirichlet Series, Some Equations of D-Branes and Rogers-Ramanujan Formulas that Link π, e and the Golden Ratio. I

Authors: Michele Nardelli, Antonio Nardelli
Comments: 153 Pages.

[7] viXra:1910.0116 [pdf] submitted on 2019-10-08 06:50:03

Prime Numbers and Its Pattern in Simple Logo

Authors: Suraj Deshmukh
Comments: 7 Pages.

In This paper we will use a simple Logo software to demonstrate a possible pattern in prime numbers. We Will see how primes show a tendency to retrace the path of other primes.
Category: Number Theory

[6] viXra:1910.0105 [pdf] replaced on 2019-10-08 11:41:30

Minimal Set for Powers of 2

Authors: Bassam Abdul-Baki
Comments: 31 Pages.

The minimal set for powers of 2 is currently nondeterministic and can be shown to be more complex than previously proposed.
Category: Number Theory

[5] viXra:1910.0081 [pdf] replaced on 2019-11-26 18:47:27

Twin Prime Conjecture (New Edition)

Authors: Toshiro Takami
Comments: 10 Pages.

I proved the Twin Prime Conjecture. All Twin Primes are executed in hexadecimal notation. It does not change in a huge number (forever huge number). In the hexagon, prime numbers are generated only at [6n -1] [6n+1]. (n is a positive integer) The probability that a twin prime will occur is 6/5 times the square of the probability that a prime will occur. If the number is very large, the probability of generating a prime number is low, but since the prime number exists forever, the probability of generating a twin prime number is very low, but a twin prime number is produced. That is, twin primes exist forever.
Category: Number Theory

[4] viXra:1910.0077 [pdf] replaced on 2023-10-09 19:51:13

Grimm's Conjecture

Authors: Radomir Majkic
Comments: 7 Pages. The paper is to clear a shortcoming observed in the conclusion of the original Grimm's Conjecture paper without altering its essentials and conclusion.

The collection of the consecutive composite integers is the composite connected, and no pair of its distinct integers may be generated by a single prime number. Composite connectedness implies the two-primes rule and the singularity propagation/breaking rule.Failure of the singularity propagation proves the Gremm's Conjecture.
Category: Number Theory

[3] viXra:1910.0075 [pdf] submitted on 2019-10-06 03:14:06

(0/0) = 0 = Refuted!

Objective: The division 0/0 has been investigated by numerous publications while the knowledge that 0/0 = 1 is still not established yet. Methods: A systematic re-analysis of the claim (0/0) = 0 was conducted again. Modus inversus was used to proof the logical consistency of such a claim. Results: The new proof provides strict evidence that 0/0=0 is not correct. Conclusions: 0/0=0 is refuted. Keywords: Division by zero, Modus inversus.
Category: Number Theory

[2] viXra:1910.0021 [pdf] submitted on 2019-10-01 15:27:10

On the Rogers-Ramanujan Identities and Continued Fractions: New Possible Mathematical Developments and Mathematical Connections with the Mass Value of Candidate “glueball” F0(1710) Meson, Other Particles and the Black Hole Entropies

Authors: Michele Nardelli, Antonio Nardelli
Comments: 210 Pages.

In the present research thesis, we have obtained various and interesting new possible mathematical results concerning the Rogers-Ramanujan identities and some continued fractions. Furthermore, we have described new possible mathematical connections with the mass value of candidate “glueball” f0(1710) meson, other particles and with the Black Hole entropies.
Category: Number Theory

[1] viXra:1910.0017 [pdf] replaced on 2019-10-02 05:02:19

On Prime Number Ⅵ2

Authors: Yuji Masuda
Comments: 1 Page.

This is primes⑥.
Category: Number Theory