Number Theory

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Recent Submissions

Any replacements are listed further down

[464] viXra:1305.0149 [pdf] submitted on 2013-05-24 01:55:13

Four Sequences of Integers Regarding Balanced Primes and Poulet Numbers

Authors: Marius Coman
Comments: 3 Pages.

A simple list of sequences of integers that reveal interesting properties of few subsets of balanced primes.
Category: Number Theory

[463] viXra:1305.0143 [pdf] submitted on 2013-05-23 12:15:00

A Proof of the Goldbach Conjecture

Authors: Julien Laurendeau
Comments: 2 Pages.

Here,I will prove the goldbach conjecture using proof by induction.
Category: Number Theory

[462] viXra:1305.0134 [pdf] submitted on 2013-05-22 15:17:24

Few Types of Chains of Primes Arising in the Study of Pseudoprimes

Authors: Marius Coman
Comments: 4 Pages.

While studying Fermat pseudoprimes I met few interesting generic forms of numbers that have the property to generate chains of primes and pseudoprimes. I list in this paper few such types of chains.
Category: Number Theory

[461] viXra:1305.0116 [pdf] submitted on 2013-05-19 08:30:03

Progress on the Goldbach Conjecture

Authors: Julien Laurendeau
Comments: 1 Page.

I found a way to prove the goldbach conjecture, but for that I needed to invent three new conjectures to whom,I still haven’t found a proof. I guess,that the person who will prove these three conjectures would be able to prove the Goldbach conjecture.
Category: Number Theory

[460] viXra:1305.0088 [pdf] submitted on 2013-05-15 12:49:43

Formulas that Generate Subsets of 3-Poulet Numbers and Few Types of Chains of Primes

Authors: Marius Coman
Comments: 3 Pages.

A simple list of sequences of products of three numbers, many of them, if not all of them, having probably an infinity of terms that are Fermat pseudoprimes to base 2 with three prime factors.
Category: Number Theory

[459] viXra:1305.0081 [pdf] submitted on 2013-05-13 06:47:57

Extended Midy's Theorem

Authors: Bassam Abdul-Baki
Comments: 5 Pages.

In mathematics, Midy's theorem, named after French mathematician E. Midy, is a statement about the decimal expansion of fractions a/p where p is a prime and a/p has a repeating decimal expansion with an even period. If the period of the decimal representation of a/p is 2n, then the digits in the second half of the repeating decimal period are the 9s complement of the corresponding digits in its first half. The Extended Midy's Theorem states that if the repeating portion of the decimal expansion of a/p is divided into k-digit numbers, then their sum is a multiple of 10^k − 1.
Category: Number Theory

[458] viXra:1305.0079 [pdf] submitted on 2013-05-13 10:57:55

A List of 13 Sequences of Carmichael Numbers Based on the Multiples of the Number 30

Authors: Marius Coman
Comments: 4 Pages.

The applications of the multiples of the number 30 in the study of Fermat pseudoprimes was for a long time one of my favourite subject of study; in this paper I shall list 13 sequences that I discovered, many of them, if not all of them, having probably an infinity of terms that are Carmichael numbers. I posted many of them on OEIS, where I analized more of their attributes; here I’ll just list them, enumerate their first few terms and present few conjectures.
Category: Number Theory

[457] viXra:1305.0023 [pdf] submitted on 2013-05-03 22:43:55

Simulation of Flexible Manufacturing System (FMS) using Fuzzy Logic

Authors: Ziaul Hassan Serneabat, Nabila Chowdhury, A.K.M. Masud
Comments: 13 Pages.

This paper focuses on the simulation of the flexible manufacturing system. Flexible manufacturing systems (FMS) are production systems consisting of identical multipurpose numerically controlled machines (workstations), automated material handling system, tools, load and unload stations, inspection stations, storage areas and a hierarchical control system. The model will prioritize the job and select the best alternative route with multi-criteria scheduling through an approach based on a fuzzy logic. There are three criteria for both the job sequencing and routing with 27 rules. With the help of the rules the sequence of the jobs are done and the best route is selected.
Category: Number Theory

[456] viXra:1305.0021 [pdf] submitted on 2013-05-04 04:05:51

The Simplest Proof of Fermat Last Theorem(1)

Authors: Chun-Xuan Jiang
Comments: 5 Pages.

Theorem .the simplest proof of Fermat last theorem.We have fermat equation x^(4p)-y^(4p)= z^(4p),where p is odd prime.We prove that if y and z are integer numbers then x,x^4 and x^p are irrational numbers.
Category: Number Theory

[455] viXra:1305.0020 [pdf] submitted on 2013-05-04 04:11:27

The Simplest Proof of Fermat Last Theorem(2)

Authors: Chun-Xuan Jiang
Comments: 7 Pages.

We have Fermat equation x^(3p)+y^(3p)=z^(3p) where p is odd prime.We prove that if y and z are integers then x,x^3,x^p are irrational numbers.
Category: Number Theory

[454] viXra:1304.0174 [pdf] submitted on 2013-04-30 12:00:57

The Identities of Ordinary Which is Leading to the Extraordinary Consequences.(elementary Aspect)

Authors: Reuven Tint
Comments: 22 Pages. Original article written in Russian.

The identity, allows obtaining range of identities as consequences, giving: 1.The alternative proof of Fermat’s Last theorem, using method of infinite descent, which is with a high degree of probability could be the solution to Fermat and proof of insolubility in natural numbers of equations for n>3. 2.Presenting another way of solutions Hilbert's seventeenth problem. 3.Version of proof is associated with the solution of the Poincare conjecture.
Category: Number Theory

[453] viXra:1304.0160 [pdf] submitted on 2013-04-29 05:33:34

Observation on Fermat's Last Theorem

Authors: Julien Laurendeau
Comments: 2 Pages.

In this paper, we are discovering something that looks a lot like Fermat's last theorem.
Category: Number Theory

[452] viXra:1304.0104 [pdf] submitted on 2013-04-22 03:15:29

Primes in the Intervals [kn,(k+1)n]

Authors: S.sambasivarao
Comments: 4 Pages. This article is communicated to "Notes on Number Theory and Discrete Mathematics"

In this paper, we prove: (a) for every integer n > 1 and a fixed integer k less than or equal to n, there exists a prime number p in betwen kn and (k + 1)n, and (b) conjectures of Legendre, Oppermann, Andrica, Brocard, and Improved version of Legendre conjecture as a particular case of (a).
Category: Number Theory

[451] viXra:1304.0102 [pdf] submitted on 2013-04-21 04:03:55

The Proof of the Twin Prime Conjecture

Authors: Ryoma Sato
Comments: 4 Pages.

I proved the twin prime conjecture with elementary number theory.
Category: Number Theory

[450] viXra:1304.0092 [pdf] submitted on 2013-04-19 01:58:17

Connections Between the Three Prime Factors of 3-Carmichael Numbers

Authors: Marius Coman
Comments: 5 Pages.

It was always obvious to me that, beside Korselt’s criterion, that gives a relation between any prime factor of a Carmichael number and the number itself, there must be a relation between the prime factors themselves; here I present a conjecture on the Carmichael numbers with three prime factors expressing the larger two prime factors as a function of the smallest one and few particular cases of connections between all three prime factors.
Category: Number Theory

[449] viXra:1304.0090 [pdf] submitted on 2013-04-18 18:20:37

Some Identities Involving four Squares II

Authors: Edigles Guedes
Comments: 1 page

ABSTRACT. We continue to develop some algebraic identities related to the power three as: (a^2 c^2+a^2 d^2+b^2 c^2+b^2 d^2 )^3=[ac(a^2-3b^2 )(c^2-3d^2 )]^2+[ad(a^2-3b^2 )(3c^2-d^2 )]^2+[bc(3a^2-b^2 )(c^2-3d^2 )]^2+[bd(3a^2-b^2 )(3c^2-d^2 )]^2.
Category: Number Theory

[448] viXra:1304.0083 [pdf] submitted on 2013-04-17 12:50:46

Some Algebraic Identities Involving four Square

Authors: Edigles Guedes
Comments: 5 pages

ABSTRACT. We have developed some algebraic identities related to power three as: 4〖(a^2 c^2+a^2 d^2+b^2 c^2+b^2 d^2)〗^3=[(a+b)(a^2-4ab+b^2 )(c+d)(c^2-4cd+d^2 )]^2+[(a+b)(a^2-4ab+b^2 )(c-d)(c^2+4cd+d^2 )]^2+[(a-b)(a^2+4ab+b^2 )(c+d)(c^2-4cd+d^2 )]^2+[(a-b)(a^2+4ab+b^2 )(c-d)(c^2+4cd+d^2 )]^2.
Category: Number Theory

[447] viXra:1304.0061 [pdf] submitted on 2013-04-13 20:06:44

An Interesting and Unexpected Property of Carmichael Numbers and a Question

Authors: Marius Coman
Comments: 2 Pages.

I was researching a kind of generalized Cunningham chains that generate, instead of primes, Fermat pseudoprimes to some base when purely by chance I noticed a property of absolute Fermat pseudoprimes, equally interesting and unexpected. By a childish simple operation, a new class of numbers is obtained from Carmichael numbers.
Category: Number Theory

[446] viXra:1304.0060 [pdf] submitted on 2013-04-14 02:46:13

Goldbach, Legendre, Brocard, Considérations élémentaires Sur Quelques Conjectures.

Authors: Olivier Massot
Comments: 83 Pages.

Symmetry proves to be a useful concept when it comes to studying some conjectures in Number theory. This study (in french) concentrates on three already well-known conjectures and the following one: For any given prime number p, there exists at least one prime number in each and every interval [kp,(k+1)p[, where k is an non-zero integer that is less than or equal to p.
Category: Number Theory

[445] viXra:1304.0058 [pdf] submitted on 2013-04-12 19:41:05

Le Théorème de Fermat-Wiles et le Critère de Eisenstein

Authors: Ahmed Idrissi Bouyahyaoui
Comments: 4 Pages. A summary is in English and the article is in French.

Let P(X) a polynomial associated to the Fermat equation x^p+y^p-z^p=0 (p is an odd prime number) and R(X) its reduction modulo k (k is a prime number): R(X)= P(X) [k]. R(X) is irreducible (Eisenstein criterion) and, therefore, P(X) is irreducible. P(X) being irreducible, it hasn't integer roots and so the associated equation x^p+y^p-z^p=0 hasn't nonzero integer solutions for all p an odd prime number.
Category: Number Theory

[444] viXra:1304.0045 [pdf] submitted on 2013-04-09 17:15:40

On the Representation of Integer Numbers by the Sum of Cube Roots

Authors: Edigles Guedes
Comments: 9 pages

We developed some formulas to represent integer numbers as the sum of cube roots.
Category: Number Theory

[443] viXra:1304.0020 [pdf] submitted on 2013-04-04 12:11:46

Talent's Error

Authors: Liu Ran
Comments: 7 Pages.

both experiment and logic analyze have demonstrate Euclid's proof is wrong
Category: Number Theory

[442] viXra:1304.0017 [pdf] submitted on 2013-04-04 08:30:26

Four Conjectures Regarding Fermat Pseudoprimes and Few Known Types of Pairs of Primes

Authors: Marius Coman
Comments: 4 Pages.

There are already known some relations between Fermat pseudoprimes and the pairs of primes [p, 2p – 1]. We will here show few relations between Fermat pseudoprimes and the pairs of primes of the type [p, 2p – 1], [p, 2p + 1], [p, sqrt(2p – 1)], respectivelly [p, k*p – k + 1].
Category: Number Theory

[441] viXra:1304.0009 [pdf] submitted on 2013-04-02 08:06:05

A New Class of Fermat Pseudoprimes and Few Remarks About Cipolla Pseudoprimes

Authors: Marius Coman
Comments: 3 Pages.

I wrote an article entitled “A formula for generating primes and a possible infinite series of Poulet numbers”; the sequence I was talking about not only that is, indeed, infinite, but is also already known as the sequence of Cipolla pseudoprimes to base 2. Starting from comparing Cipolla pseudoprimes and some of my notes I discovered a new class of pseudoprimes.
Category: Number Theory

[440] viXra:1304.0001 [pdf] submitted on 2013-04-01 07:39:56

Primality Criteria for Specific Classes of Proth Numbers

Authors: Predrag Terzic
Comments: 2 Pages.

Polynomial time prime testing algorithms for specific classes of Proth numbers are introduced
Category: Number Theory

[439] viXra:1303.0195 [pdf] submitted on 2013-03-26 00:26:30

Generalization of Lucas-Lehmer-Riesel Test

Authors: Predrag Terzic
Comments: 2 Pages.

Generalization of Lucas-Lehmer-Riesel primality test is introduced .
Category: Number Theory

[438] viXra:1303.0191 [pdf] submitted on 2013-03-25 10:57:13

Two Conjectures on Primality

Authors: Predrag Terzic
Comments: 2 Pages.

Generalizations of Wilson's theorem and Kilford's theorem are introduced .
Category: Number Theory

[437] viXra:1303.0190 [pdf] submitted on 2013-03-25 11:02:22

Four Prime-Generating Recurrences

Authors: Predrag Terzic
Comments: 3 Pages.

Prime number generating recurrences are introduced .
Category: Number Theory

[436] viXra:1303.0183 [pdf] submitted on 2013-03-24 04:26:14

On The Particular Distribution Of Prime Numbers

Authors: Keith Hodebourg
Comments: 15 Pages.

On the particular distribution of prime numbers is a case to be treated in several parts. In the first place, I will treat the prime identity Δ, which is the method that allows one to discern with certainty prime numbers γ, of strong non-prime numbers ω, and non-prime numbers μ, amongst the series of natural wholes A, as in :.....................
Category: Number Theory

[435] viXra:1303.0182 [pdf] submitted on 2013-03-24 04:28:16

On Goldbach's Conjecture

Authors: Keith Hodebourg
Comments: 01 Pages.

The german mathematician Christian Goldbach, in a letter dated 1742 to Leonhard Euler, announced a conjecture which affirm that any even number greater than or equal to 4 is the sum of two prime numbers........................
Category: Number Theory

[434] viXra:1303.0181 [pdf] submitted on 2013-03-24 04:30:33

On Cramers Conjecture

Authors: Keith Hodebourg
Comments: 01 Pages.

In 1937 the Swedish mathematician Harald Cramer put forth the hypothesis that there always exists a prime number between X and X (InX)2, I respons in this way :..............
Category: Number Theory

[433] viXra:1303.0180 [pdf] submitted on 2013-03-24 04:33:02

On The Twin Prime Numbers Conjecture

Authors: Keith Hodebourg
Comments: 01 Pages.

The twin prime numbers conjecture announces the hypothesis that there exists an infinite of twin prime numbers, I respond in this way :.........
Category: Number Theory

[432] viXra:1303.0135 [pdf] submitted on 2013-03-19 02:43:19

A Conjecture About a Large Subset of Carmichael Numbers Related to Concatenation

Authors: Marius Coman
Comments: 5 Pages.

Though the method of concatenation has it’s recognised place in number theory, is rarely leading to the determination of characteristics of an entire class of numbers, which is not defined only through concatenation. We present here a property related to concatenation that appears to be shared by a large subset of Carmichael numbers.
Category: Number Theory

[431] viXra:1303.0113 [pdf] submitted on 2013-03-15 09:39:12

Structure de Groupe Abélien Sur L'ensemble Des Couples (6n 1,6n + 1)

Authors: M. MADANI Bouabdallah
Comments: 07 Pages. French language

The set of (6n - 1,6n +1)is an abelian group for n rational integer.
Category: Number Theory

[430] viXra:1303.0109 [pdf] submitted on 2013-03-14 17:52:41

Divisor Function: Elementary Formulas and Asymptotic

Authors: Edigles Bezerra Guedes
Comments: 7 pages

We discovery some formulas for the divisor function, derived from a Vinogradov’s formula and definitions these function, including the Ramanujan’s sum. As well, we have developed a formula asymptotic, using the Euler-Maclaurin summation formula.
Category: Number Theory

[429] viXra:1303.0088 [pdf] submitted on 2013-03-12 03:24:32

Foundations of Santilli Isonumber Theory

Authors: Chun-Xuan Jiang
Comments: 413 Pages.

1.Foudations of Santilli isonumber theory.I:isonumber theory of the first kind;2.Santilli isonumber theory.II:isonumber theory of the second kind;3.Fermat last theorem and its applications;4.the proofs of binary Goldbach theorem using only partial primes;5.Santilli isocryptographic theory.Disproofs of Riemann hypothesis.
Category: Number Theory

[428] viXra:1303.0081 [pdf] submitted on 2013-03-11 07:14:43

A Conjecture Regarding the Relation Between Carmichael Numbers and the Sum of Their Digits

Authors: Marius Coman
Comments: 4 Pages.

Though they are a fascinating class of numbers, there are very many properties of Carmichael numbers still unstudied enough. I have always thought there is a connection between these numbers and the sum of their digits (few of them are also Harshad numbers). I try here to highlight such a possible connection.
Category: Number Theory

[427] viXra:1303.0048 [pdf] submitted on 2013-03-07 11:32:32

An Elementary Proof of Legendre's Conjecture

Authors: Edigles Bezerra Guedes
Comments: 6 pages

We prove the Legendre’s conjecture: given an integer, n>0, there is always one prime, p, such that n^2<p<(n+1)^2, using the prime-counting function and the Bertrand’s Postulate.
Category: Number Theory

[426] viXra:1303.0047 [pdf] submitted on 2013-03-07 11:35:37

An Elementary Proof of Oppermann's Conjecture

Authors: Edigles Bezerra Guedes
Comments: 7 pages

We prove the Oppermann’s conjecture: given an integer, n>1, there is, at least, one prime between n^2-n and n^2, and, at least, another prime between n^2 and n^2+n, using the prime-counting function and the Bertrand’s Postulate.
Category: Number Theory

[425] viXra:1303.0031 [pdf] submitted on 2013-03-06 04:31:54

Few Recurrent Series Based on the Difference Between Succesive Primes

Authors: Marius Coman
Comments: 6 Pages.

Despite the development of computer systems, the chains of succesive primes obtained through an iterative formula yet have short lenghts; for instance, the largest known chain of primes in arithmetic progression is an AP-26. We present here few formulas that might lead to interesting chains of primes.
Category: Number Theory

[424] viXra:1303.0019 [pdf] submitted on 2013-03-04 08:27:01

Primes for a Caveman

Authors: Nikolay Dementev
Comments: 4 Pages.

Algorithm for determining whether given number is a prime or a composite is conjectured. The algorithm implies neither division operation, nor the counting to more than two to be an a priori knowledge.
Category: Number Theory

Recent Replacements

[177] viXra:1304.0104 [pdf] replaced on 2013-04-22 22:15:14

Primes in the Intervals [kn,(k+1)n]

Authors: S. Sambasivarao
Comments: 4 Pages. This paper is communicated to "Notes on Number Theory and Discrete Mathematics"

Abstract. In this paper, we prove: (a) for every integer n > 1 and a fixed integer k less than or equal to n, there exists a prime number p in between kn and (k + 1)n, and (b) conjectures of Legendre, Oppermann, Andrica, Brocard, and Improved version of Legendre conjecture as a particular case of (a).
Category: Number Theory

[176] viXra:1304.0070 [pdf] replaced on 2013-04-16 11:18:26

Le Théorème de Fermat-Wiles et le Critère de Eisenstein V.2

Authors: Ahmed Idrissi Bouyahyaoui
Comments: 4 Pages. A summary is in English and the article is in French.

Let P(X) a polynomial associated to the Fermat equation x^p+y^p-z^p=0 (p is an odd prime number) and R(X) its reduction modulo k (k is a prime number): R(X)= P(X) [k]. R(X) is irreducible (Eisenstein criterion) and, therefore, P(X) is irreducible. P(X) being irreducible, it hasn't integer roots and so the associated equation x^p+y^p-z^p=0 hasn't nonzero integer solutions for all p odd prime number.
Category: Number Theory

[175] viXra:1304.0060 [pdf] replaced on 2013-04-24 08:27:28

Goldbach, Legendre, Brocard, Considérations élémentaires Sur Quelques Conjectures.

Authors: Olivier Massot
Comments: Corrections page 47/85

Symmetry proves to be a useful concept when it comes to studying some conjectures in Number theory. This study (in french) concentrates on three already well-known conjectures and the following one: For any given prime number p, there exists at least one prime number in each and every interval [kp,(k+1)p[, where k is an non-zero integer that is less than or equal to p.
Category: Number Theory

[174] viXra:1304.0060 [pdf] replaced on 2013-04-22 09:13:49

Goldbach, Legendre, Brocard, Considérations élémentaires Sur Quelques Conjectures.

Authors: Olivier Massot
Comments: 85 Pages.

Symmetry proves to be a useful concept when it comes to studying some conjectures in Number theory. This study (in french) concentrates on three already well-known conjectures and the following one: For any given prime number p, there exists at least one prime number in each and every interval [kp,(k+1)p[, where k is an non-zero integer that is less than or equal to p.
Category: Number Theory

[173] viXra:1304.0058 [pdf] replaced on 2013-04-18 04:34:26

Le Théorème de Fermat-Wiles et le Critère de Eisenstein

Authors: Ahmed Idrissi Bouyahyaoui
Comments: 4 Pages. Summary is in English and article is in French.

Let P(X) a polynomial associated to the Fermat's equation x^p+y^p-z^p=0 (p is an odd prime number) and R(X) its reduction modulo k (k is a prime number): R(X)= P(X) [k]. R(X) is irreducible (Eisenstein criterion) and, therefore, P(X) is irreducible. P(X) being irreducible, it hasn't integer roots and so the associated equation x^p+y^p-z^p=0 hasn't nonzero integer solutions for all odd prime number p.
Category: Number Theory

[172] viXra:1304.0020 [pdf] replaced on 2013-04-06 09:37:33

Talent's Error

Authors: Liu Ran
Comments: 7 Pages.

both experiment and logic analyze have demonstrate Euclid's proof is wrong
Category: Number Theory

[171] viXra:1304.0020 [pdf] replaced on 2013-04-04 21:20:34

Talent's Error

Authors: Liu Ran
Comments: 7 Pages.

both experiment and logic analyze have demonstrate Euclid's proof is wrong
Category: Number Theory

[170] viXra:1303.0091 [pdf] replaced on 2013-03-17 06:39:04

Minorer le Nombre de Décomposants de Goldbach

Authors: Denise Chemla
Comments: 10 Pages.

Using a minoration-majoration for each prime number of the non-Goldbach components of an odd number, we try to minorate Goldbach components number.
Category: Number Theory