| viXra.org > Number Theory > 2210 |
 |
 |
| viXra.org > Number Theory > 2210 |
|
|
[14] viXra:2210.0164 [pdf] submitted on 2022-10-31 01:03:58
Authors: Victor Sorokine
Comments: 4 Pages.
In a number system with a prime base n>2, among n-1 powers of dn (d=1, u2026 n-1) there is a number whose second (from the end of the number) digit is not equal to 0. (The key lemma in the simplest proof of Fermat's Last Theorem.)
Category: Number Theory
[13] viXra:2210.0149 [pdf] submitted on 2022-10-30 01:21:26
Authors: Shazly Abdullah
Comments: 7 Pages.
The work of José María Grau and Antonio M. Oller-marcén has been generalized. Two proofs are presented to prove the generalization. The first is based on the binomial theorem and elementary algebra, and the second is based on the difference theorem and properties of congruence in particular.
Category: Number Theory
[12] viXra:2210.0131 [pdf] replaced on 2024-01-25 22:05:03
Authors: Andrea Berdondini
Comments: 4 Pages.
Abstract: the aim of this article is to find the arrangement in which prime numbers less than or equal to a number N occupy the greatest possible number of consecutive positions. Solving this problem is fundamental in understanding what the maximum gap is between two prime numbers and therefore being able to prove the conjectures relating to this problem: such as the Legendre conjecture.
Category: Number Theory
[11] viXra:2210.0119 [pdf] submitted on 2022-10-25 00:46:34
Authors: Theophilus Agama
Comments: 4 Pages. The paper uses the notion of a disc induced by arithmetic function to relate perfect numbers with abundant numbers
In this paper we investigate some properties of perfect numbers and associated sequences using the notion of the disc induced by the sum-of-the-divisor function $sigma$. We reveal an important relationship between perfect numbers and abundant numbers.
Category: Number Theory
[10] viXra:2210.0107 [pdf] replaced on 2022-10-27 00:54:05
Authors: Rachid Annouaoui
Comments: 9 Pages. In English
This is an attempt at the proof of Goldbach Conjecture.
Category: Number Theory
[9] viXra:2210.0105 [pdf] submitted on 2022-10-24 02:40:15
Authors: Victor Sorokine
Comments: 4 Pages.
Proof-consequence, no calculations. Among the n-1 equalities equivalent to Fermat's basic equality, obtained by multiplying it by the numbers d (d=1, u2026, n-1) to the power of n^2, there is an equality that does not hold for the third digits.
Category: Number Theory
[8] viXra:2210.0090 [pdf] submitted on 2022-10-20 01:39:28
Authors: Giovanni Di Savino
Comments: 5 Pages. In Italian
Thales taught us that if reported on a plane, one can measure the inaccessible and the unattainable; our inaccessible and unreachable to measure is the umpteenth prime number which is the sum of the distances that separate its minor prime numbers which is as large, inaccessible and unattainable as the quantity of multiples present between two consecutive primes.
Category: Number Theory
[7] viXra:2210.0087 [pdf] submitted on 2022-10-20 01:47:02
Authors: Jean-Yves Boulay
Comments: 13 Pages.
An unprecedented numbering of the twenty proteinogenic amino acids, itself deduced from a logical numbering of the sixty-four DNA triplets, reveals connections between the mechanism of the genetic code, of the field of Biology, and the number theory field, of which more precisely the notion of ultimate number, one of the four classes of Mathematics entities proposed to constitute the set of whole numbers. These connections are revealed in an physico-arithmetic organization of the genetic code in various ratios of 3/2 value as global configurations.
Category: Number Theory
[6] viXra:2210.0054 [pdf] submitted on 2022-10-14 01:38:14
Authors: Theophilus Agama, Berndt Gensel
Comments: 13 Pages. This paper resolves Lemoine's conjecture in an asymptotical sense using the method of complex circles of partition.
Using the methods of the complex circles of partition (cCoPs), we study textit{interior} and textit{exterior} points of such structures in the complex plane. With similarities to textit{quotient groups} inside of the group theory we define textit{quotient cCoPs}. With it we can prove an asymptotic version of the textbf{Lemoine Conjecture}.
Category: Number Theory
[5] viXra:2210.0045 [pdf] submitted on 2022-10-11 02:19:52
Authors: Olvine Dsouza
Comments: 15 Pages. (Correction made by viXra Admin)
Where z is the product of two multiplied prime numbers, that is p and q. If the p and q as prime numbers having larger digits like 100, 500 and more digits, then it is easier to multiply those two large numbers( p × q) to get z, but it is harder, more time consuming and can be a non trivial solution of reversing it back and find the factors of n. Introducing a new method of finding p and q of given n. This method gives the fast result in finding either p or q of given z.
Category: Number Theory
[4] viXra:2210.0036 [pdf] submitted on 2022-10-09 03:15:51
Authors: Giovanni Di Savino
Comments: 2 Pages.
Natural numbers, primes or compounds are infinite, they can be known numbers and, if they are large numbers composed of many digits, they are not yet known but: known or not all exist and are the result of mathematical operations reported in equations.
Category: Number Theory
[3] viXra:2210.0029 [pdf] submitted on 2022-10-07 16:18:58
Authors: Richard J. Mathar
Comments: 34 Pages.
We list non-negative integer solutions (x,y,z,w) to the 5-term exponential diophantine equation 1 +p_1^x +p_2^y + p_3^z = w^2 for three distinct primes p_1 < p_2 < p_3 <= 113 obtained by exhaustive search in the exponents x, y, z <= 60.
Category: Number Theory
[2] viXra:2210.0025 [pdf] replaced on 2022-10-22 05:04:16
Authors: Zhi Li, Hua Li
Comments: 5 Pages.
Dubner's conjecture was proposed by American electrical engineer and mathematical researcher Harvey Dubner (1928 — 2019) in 1996, that is, all sufficiently large even numbers (greater than 4208) are the sum of some two twin prime numbers.Since there is no mathematical model for prime numbers to be completely accurate, prime numbers are randomly distributed on the number axis. The distribution of prime numbers in the latest research results is deterministic random distribution, so the problems related to prime numbers can be studied, analyzed and proved by using probability statistics methods.In this paper, the Dubner's conjecture is proved by the method of probability and statistics.
Category: Number Theory
[1] viXra:2210.0013 [pdf] replaced on 2022-11-13 16:15:27
Authors: Theophilus Agama, Berndt Gensel
Comments: 12 Pages.
In this paper we use the former of the authors developed theory of circles of partition to investigate possibilities to prove the binary Goldbach as well as the Lemoine conjecture. We state the squeeze principle and its consequences if the set of all odd prime numbers is the base set. With this tool we can prove asymptotic versions of the binary Goldbach as well as the Lemoine conjecture.
Category: Number Theory
| Third-Party Links: |
|