Number Theory

Previous months:
2007 - 0703(3) - 0706(2)
2008 - 0807(1) - 0809(1) - 0810(1) - 0812(2)
2009 - 0901(2) - 0904(2) - 0907(2) - 0908(4) - 0909(1) - 0910(2) - 0911(1) - 0912(3)
2010 - 1001(3) - 1002(1) - 1003(55) - 1004(50) - 1005(36) - 1006(7) - 1007(11) - 1008(16) - 1009(21) - 1010(8) - 1011(7) - 1012(13)
2011 - 1101(14) - 1102(7) - 1103(13) - 1104(3) - 1105(1) - 1106(2) - 1107(1) - 1108(2) - 1109(2) - 1110(5) - 1111(4) - 1112(4)
2012 - 1201(2) - 1202(13) - 1203(7) - 1204(9) - 1205(7) - 1206(6) - 1207(5) - 1208(5) - 1209(11) - 1210(15) - 1211(10) - 1212(4)
2013 - 1301(5) - 1302(10) - 1303(16) - 1304(15) - 1305(12) - 1306(13) - 1307(25) - 1308(11) - 1309(9) - 1310(13) - 1311(16) - 1312(21)
2014 - 1401(20) - 1402(11) - 1403(23) - 1404(10) - 1405(17) - 1406(21) - 1407(35) - 1408(52) - 1409(47) - 1410(18) - 1411(18) - 1412(20)
2015 - 1501(15) - 1502(16) - 1503(4)

Recent submissions

Any replacements are listed further down

[889] viXra:1503.0028 [pdf] submitted on 2015-03-04 01:48:36

Another Infinite Sequence Based on Mar Function that Abounds in Primes and Semiprimes

Authors: Marius Coman
Comments: 4 Pages.

In one of my previous paper, namely “The mar reduced form of a natural number”, I introduced the notion of mar function, which is, essentially, nothing else than the digital root of a number, and I also presented, in another paper, a sequence based on mar function that abounds in primes. In this paper I present another sequence, based on a relation between a number and the value of its mar reduced form (of course not the intrisic one), sequence that seem also to abound in primes and semiprimes.
Category: Number Theory

[888] viXra:1503.0026 [pdf] submitted on 2015-03-03 16:08:31

The Notions of Mar Constants and Smarandache Mar Constants

Authors: Marius Coman
Comments: 8 Pages.

In one of my previous paper, “The mar reduced form of a natural number”, I introduced the notion of mar function, which is, essentially, nothing else than the digital root of a number, but defined as an aritmethical function, on the operations of addition, multiplication etc. in such way that it could be used in various applications (Diophantine equations, divizibility problems and others). In this paper I present two notions, useful in Diophantine analysis of Smarandache concatenated sequences or different classes of numbers (sequences of squares, cubes, triangular numbers, polygonal numbers, Devlali numbers, Demlo numbers etc).
Category: Number Theory

[887] viXra:1503.0025 [pdf] submitted on 2015-03-03 16:49:58

An Infinite Sequence Based on Mar Function that Abounds in Primes

Authors: Marius Coman
Comments: 4 Pages.

I introduced, in one of my previous paper, namely “The mar reduced form of a natural number”, the notion of mar function, which is, essentially, nothing else than the digital root of a number, but defined as an aritmethical function, in such way that it could be used in various applications (Diophantine analysis of different types of numbers etc). In this paper I present a sequence based on a relation between a number and the value of its mar reduced form (of course not the intrisic one), sequence that seem to be interesting because many of its terms are primes or ar equal to 1 and very few composites.
Category: Number Theory

[886] viXra:1503.0005 [pdf] submitted on 2015-03-01 07:46:41

New Formula of the Mobius Function

Authors: T.Nakashima
Comments: 1 Page.

This is the new formula of the mobius function.
Category: Number Theory

[885] viXra:1502.0200 [pdf] submitted on 2015-02-22 12:36:35

Estimates for Von Mangoldt, Second Chebyshev and RIEMANN’S J Functions

Authors: Edigles Guedes
Comments: 7 pages.

We prove some estimates for von Mangold function, second Chebyshev function and Riemann’s J function by elementary methods.
Category: Number Theory

[884] viXra:1502.0198 [pdf] submitted on 2015-02-22 14:58:04

A Note on a New Prime Gap Constant

Authors: Waldemar Puszkarz
Comments: 2 Pages.

We propose a new mathematical constant related to the gaps between consecutive primes obtained by concatenating the digits in the prime gap numbers.
Category: Number Theory

[883] viXra:1502.0197 [pdf] submitted on 2015-02-22 07:53:46

The Conjecture of Erdos-Strauss and Its Application in Demonstrating the Twin Primes Supported by the Bayes´ Theorem.

Authors: Rodolfo A. Nieves Rivas
Comments: 7 Pages.

In this brief paper we present the necessary and sufficient conditions within the solution of the Erdos-Straus conjecture when (n) takes the values of any twin prime. Then we conclude with a table for its visualization and analysis proving by the Bayes' theorem that the twin primes are infinite.
Category: Number Theory

[882] viXra:1502.0196 [pdf] submitted on 2015-02-22 09:15:59

Three Proofs for Legendre's Conjecture

Authors: Edigles Guedes
Comments: 7 pages.

We write three proves for Legendre's conjecture: given an integer, n > 0, there is always one prime number, p, such that n^2 < p < (n + 1)^2, using the prime-counting function, the Bertrand's postulate and the Hardy-Wright's estimate.
Category: Number Theory

[881] viXra:1502.0195 [pdf] submitted on 2015-02-22 06:05:29

The Method of Structurization of a Set of Positive Integers and Its Application to the Primality Testing Algorithm}

Authors: Alexander Fedorov
Comments: 37 Pages.

\ heIn this paper is offered and theoretically is based the algorithm permissive with the lp of small number of arithmetic operations with arbitrary positive integer(N) to answer a question : is N composite or prime? The algorithm has a high operational speed which depends a little on value N ,and is based on The method of structurization of a set of positive integers (Np) developed by the author. In limits of a framework of this method is defined a special set of the structured integers (Ns) in which it becomes possibility for testing of any structured integers (Sn) on a membership of a set of composite structured integers (Nsc). Between by Np and Ns is established one-to-one correspondence : composite structured integers (Snc) are corresponded to composite positive integers . Prime structured integers are corresponded to prime positive integers Thus for testing arbitrary (N) it is necessary to map it into . Then we test obtained on a membership of If Sn is a member of then the output follows that tested N is also composite.If Sn is not a member of Nsc then the output follows that tested $N$ is also prime , since if Sn is not composite then it is prime ,tertiary is not given.
Category: Number Theory

[880] viXra:1502.0140 [pdf] submitted on 2015-02-16 16:09:21

Approximations for Prime Numbers and Superposition of Integer Sequences II

Authors: Edigles Guedes
Comments: 5 pages.

I proved two approximations for prime numbers using trigonometric sums.
Category: Number Theory

[879] viXra:1502.0136 [pdf] submitted on 2015-02-16 19:49:22

Investigations on the Chebyshev Functions

Authors: Edigles Guedes
Comments: 3 pages.

I proved two lower bound for rst Chebyshev function and leave a conjecture on prime numbers.
Category: Number Theory

[878] viXra:1502.0134 [pdf] submitted on 2015-02-16 21:36:07

A Short Proof for Oppermann's Conjecture

Authors: Edigles Guedes
Comments: 3 pages.

We write a prove for Oppermann's conjecture using the Hardy-Wright's estimate for prime-counting function.
Category: Number Theory

[877] viXra:1502.0131 [pdf] submitted on 2015-02-16 13:02:14

Approximations for Prime Numbers and Superposition of Integer Sequences I

Authors: Edigles Guedes
Comments: 7 pages.

I proved some three approximations for prime numbers.
Category: Number Theory

[876] viXra:1502.0078 [pdf] submitted on 2015-02-11 04:08:43

Chunxuan Jiang a Controversial Chinese Mathematician

Authors: Zhenghai Jiang
Comments: 5 Pages.

Chunxuan Jiang is a controversial mathematician in the history of moden mathematics.In China Jiang work was completely repelled and been considered as pseudoscience.Jiang dedicates his work alma mater(Beihang university) and China which rejected.
Category: Number Theory

[875] viXra:1502.0039 [pdf] submitted on 2015-02-04 23:56:09

New Axiom for ZFC

Authors: Posey Bonennnn, Posey Bonennn, Posey Bonenn, Posey Bonen
Comments: 1 Page.

ZFC IS WEEEEKK NEEDS MORE POWER> I CAN FIX THAT> I INTRODUCE A GENIUS AXIUM THAT SOLVES SEVERAL NOW TRIVIAL CONJECTURES THAT HAVE BEEN LONG STANDING. IT ALSO MAKES POSSIBLY IT TO PROOVE CONTINUOUM HYPOTHESIS AND THAT ZFC IS COMPLETE WITH MY NEW AXIUM>>>\\\\\\ THE AXEIUM IS THAT ZFC IS COMPLETE>
Category: Number Theory

[874] viXra:1502.0038 [pdf] submitted on 2015-02-04 23:57:46

New Axiom Complete ZFC

Authors: Posey Bonennn
Comments: 1 Page.

ZFC IS WEEEEKK NEEDS MORE POWER> I CAN FIX THAT> I INTRODUCE A GENIUS AXIUM THAT SOLVES SEVERAL NOW TRIVIAL CONJECTURES THAT HAVE BEEN LONG STANDING. IT ALSO MAKES POSSIBLY IT TO PROOVE CONTINUOUM HYPOTHESIS AND THAT ZFC IS COMPLETE WITH MY NEW AXIUM>>>\\\\\\ THE AXEIUM IS THAT ZFC IS COMPLETE>
Category: Number Theory

[873] viXra:1502.0037 [pdf] submitted on 2015-02-05 02:10:04

The MC Function and Other Three Smarandache Type Sequences, Diophantine Analysis

Authors: Marius Coman
Comments: 2 Pages.

In seven of my previous papers, I defined the MC function and I showed some of its possible applications. In this paper I present new interesting properties of other three Smarandache type sequences analyzed through the MC function.
Category: Number Theory

[872] viXra:1502.0020 [pdf] submitted on 2015-02-02 18:42:28

Conjecture that Relates Both the Lesser and the Larger Term of a Pair of Twin Primes to the Same Number Through Two Different Functions

Authors: Marius Coman
Comments: 1 Page.

In this paper I conjecture that for any pair of twin primes p and p + 2 there exist an odd positive integer n such that the value of Smarandache function for n is equal to p and the value of MC function for n is equal to p + 2.
Category: Number Theory

[871] viXra:1502.0008 [pdf] submitted on 2015-02-01 07:16:14

A Classification of Primes in Four Classes Using the MC Function

Authors: Marius Coman
Comments: 2 Pages.

In few of my previous papers I defined the MC function. In this paper I make a classification of primes in four classes using a formula involving this function, id est the formula p + MC(p + 2) – 5, where p is prime. The classification is strict, a prime can not belong simultaneously to two classes.
Category: Number Theory

[870] viXra:1502.0001 [pdf] submitted on 2015-02-01 01:05:16

Proofs of the Goldbach Theorem and the Twin Prime Theorem

Authors: Jian Ye
Comments: 9 Pages.

The Goldbach theorem and the twin prime theorem are homologous.the paper from the prime origin,derived the equations of the twin prime theorem and the Goldbach theorem,and it revealed the equivalence between the Goldbach theorem and the generalized twin prime theorem.
Category: Number Theory

[869] viXra:1501.0256 [pdf] submitted on 2015-01-31 21:32:13

On the MC Function, the Squares of Primes and the Pairs of Twin Primes

Authors: Marius Coman
Comments: 2 Pages.

In few of my previous papers I defined the MC function. In this paper I make two conjectures, involving this function, the squares of primes and the pairs of twin primes.
Category: Number Theory

[868] viXra:1501.0252 [pdf] submitted on 2015-01-30 12:14:34

Version of Proof of the Fermat's Last Theorem

Authors: Michael Pogorsky
Comments: 6 Pages. The third version of analogously based proofs of FLT

This is the shortest and most direct version of proofs of FLT based on deduced for two main cases of the equation a^n+b^n=c^n polynomial expressions a=uwv+v^n; b=uwv+w^n; c=uwv+v^n+w^n. Contradiction revealed in the polynomials does not allow them to become integer numbers and proves the Theorem.
Category: Number Theory

[867] viXra:1501.0232 [pdf] submitted on 2015-01-26 17:28:17

Hardy-Littlewood Conjecture and Exceptional real Zero

Authors: JinHua Fei
Comments: 9 Pages.

In this paper, we assume that Hardy-Littlewood Conjecture, we got a better upper bound of the exceptional real zero for a class of module.
Category: Number Theory

[866] viXra:1501.0201 [pdf] submitted on 2015-01-21 17:08:45

High Degree Diophantine Equation by Classical Number Theory

Authors: Wu Sheng-Ping
Comments: 6 Pages.

The main idea of this article is simply calculating integer functions in module. The algebraic in the integer modules is studied in completely new style. By analysis in module and a careful constructing, a condition of non-solution of Diophantine Equation $a^p+b^p=c^q$ is proved that: $(a,b)=(b,c)=1,a,b>0,p,q>12$, $p$ is prime. The proof of this result is mainly in the last two sections.
Category: Number Theory

[865] viXra:1501.0192 [pdf] submitted on 2015-01-20 04:15:40

The Fermat's Last Theorem

Authors: Nicolae Bratu
Comments: 13 Pages.

This article generalizes and makes some additions to the method used in this demonstration theorem for exponents 3 and 5. In this regard, this paper presents a complete algebraic demonstration of Fermat’s Last Theorem.
Category: Number Theory

[864] viXra:1501.0150 [pdf] submitted on 2015-01-13 17:48:08

On the Sum of Three Consecutive Values of the MC Function

Authors: Marius Coman
Comments: 2 Pages.

In a previous paper I defined the MC(x) function in the following way: Let MC(x) be the function defined on the set of odd positive integers with values in the set of primes such that: MC(x) = 1 for x = 1; MC(x) = x, for x prime; for x composite, MC(x) has the value of the prime which results from the following iterative operation: let x = p(1)*p(2)*...*p(n), where p(1),..., p(n) are its prime factors; let y = p(1) + p(2) +...+ p(n) – (n – 1); if y is a prime, then MC(x) = y; if not, then y = q(1)*q(2)*...*q(m), where q(1),..., q(m) are its prime factors; let z = q(1) + q(2) +...+ q(m) – (m – 1); if z is a prime, then MC(x) = z; if not, it is iterated the operation until a prime is obtained and this is the value of MC(x). In this paper I present a property of this function.
Category: Number Theory

[863] viXra:1501.0146 [pdf] submitted on 2015-01-14 01:42:15

The MC Function and Three Smarandache Type Sequences, Diophantine Analysis

Authors: Marius Coman
Comments: 3 Pages.

In two of my previous papers, namely “An interesting property of the primes congruent to 1 mod 45 and an ideea for a function” respectively “On the sum of three consecutive values of the MC function”, I defined the MC function. In this paper I present new interesting properties of three Smarandache type sequences analyzed through the MC function.
Category: Number Theory

[862] viXra:1501.0141 [pdf] submitted on 2015-01-13 05:05:44

An Interesting Property of the Primes Congruent to 1 Mod 45 and an Ideea for a Function

Authors: Marius Coman
Comments: 3 Pages.

In this paper I show a certain property of the primes congruent to 1 mod 45 related to concatenation, namely the following one: concatenating two or three or more of these primes are often obtaied a certain kind of composites, id est composites of the form m*n, where m and n are not necessarily primes, having the property that m + n - 1 is a prime number. Plus, I present an ideea for a function which be interesting to study.
Category: Number Theory

[861] viXra:1501.0129 [pdf] submitted on 2015-01-12 15:53:42

The Prime Number Formulas

Authors: Ke Xiao
Comments: 6 Pages.

Abstract There are many proposed partial prime number formulas, however, no formula can generate all prime numbers. Here we show three formulas which can obtain the entire prime numbers set from the positive integers, based on the Möbius function plus the “omega” function, or the Omega function, or the divisor function.
Category: Number Theory

[860] viXra:1501.0125 [pdf] submitted on 2015-01-12 10:18:33

A Proof of the Abc Conjecture (After Second Modification)

Authors: Zhang Tianshu
Comments: 13 Pages.

We first get rid of three kinds from A+B=C according to their respective odevity and gcf (A, B, C) =1. After that, expound relations between C and raf (ABC) by the symmetric law of odd numbers. Finally we have proven C≤Cε [raf (ABC)] 1+ ε in which case A+B=C, where gcf (A, B, C) =1.
Category: Number Theory

[859] viXra:1501.0121 [pdf] submitted on 2015-01-11 16:01:11

Three Functions Based on the Digital Sum of a Number and Ten Conjectures

Authors: Marius Coman
Comments: 3 Pages.

In this paper I present three functions based on the digital sum of a number which might be interesting to study and ten conjectures. These functions are: (I) F(x) defined as the digital sum of the number 2^x – x^2; (II) G(x) equal to F(x) – x and (III) H(x) defined as the digital sum of the number 2^x + x^2.
Category: Number Theory

[858] viXra:1501.0068 [pdf] submitted on 2015-01-05 06:44:12

A Proof of the Abc Conjecture (After First Modification)

Authors: Zhang Tianshu
Comments: 12 Pages.

We first get rid of three kinds from A+B=C according to their respective odevity and gcf (A, B, C) =1. After that, expound relations between C and raf (ABC) by the symmetric law of odd numbers. Finally we have proven C≤Cε [raf (ABC)] 1+ ε in which case A+B=C, where gcf (A, B, C) =1.
Category: Number Theory

[857] viXra:1501.0067 [pdf] submitted on 2015-01-05 07:14:57

A Proof of the Beal’s Conjecture (After fifth Modification)

Authors: Zhang Tianshu
Comments: 23 Pages.

First we classify A, B and C according to their respective odevity, and ret rid of two kinds from AX+BY=CZ. Then affirm AX+BY=CZ in which case A, B and C have a common prime factor by concrete examples. After that, prove AX+BY≠CZ in which case A, B and C have not any common prime factor by the mathematical induction with the aid of the symmetric law of odd numbers after the decomposition of the inequality. Finally, we have proven that the Beal’s conjecture holds water after the comparison between AX+BY=CZ and AX+BY≠CZ under the given requirements.
Category: Number Theory

[856] viXra:1501.0050 [pdf] submitted on 2015-01-04 03:48:24

Odd Number Sum Theorem

Authors: Maik Becker-Sievert
Comments: 1 Page.

Every odd number y is the sum of n following numbers while n is a divisor of y.
Category: Number Theory

[855] viXra:1501.0026 [pdf] submitted on 2015-01-03 01:06:09

The Goldbach Theorem and the Twin Prime Theorem

Authors: Jian Ye
Comments: 5 Pages.

The Goldbach theorem and the twin prime theorem is homologous.the paper from the prime origin,derived the equations of the twin prime theorem and the Goldbach theorem,and it revealed the equivalence between the Goldbach theorem and the generalized twin prime theorem.
Category: Number Theory

Replacements of recent Submissions

[408] viXra:1503.0005 [pdf] replaced on 2015-03-04 03:13:20

New Formula of the Mobius Function

Authors: T.Nakashima
Comments: 2 Pages.

This is the new formula of the mobius function.
Category: Number Theory

[407] viXra:1502.0078 [pdf] replaced on 2015-02-17 05:25:35

Chunxuan Jiang-a Tragic Chinese Mathematician

Authors: Zhenghai Song
Comments: 5 Pages.

Chunxuan Jiang is a tragic mathematician in the history of modern mathematics.In China Jiang work was completely repelled and been considered as pseudoscience.Jiang dedicates his work to alma mater (Beihang university) and China which rejected.
Category: Number Theory

[406] viXra:1501.0201 [pdf] replaced on 2015-02-28 15:07:30

High Degree Diophantine Equation by Classical Number Theory

Authors: Wu Sheng-Ping
Comments: 6 Pages.

The main idea of this article is simply calculating integer functions in module. The algebraic in the integer modules is studied in completely new style. By analysis in module and a careful constructing, a condition of non-solution of Diophantine Equation $a^p+b^p=c^q$ is proved that: $(a,b)=(b,c)=1,a,b>0,p,q>12$, $p$ is prime. The proof of this result is mainly in the last two sections.
Category: Number Theory

[405] viXra:1501.0201 [pdf] replaced on 2015-02-05 16:43:42

High Degree Diophantine Equation by Classical Number Theory

Authors: Wu Sheng-Ping
Comments: 6 Pages.

The main idea of this article is simply calculating integer functions in module. The algebraic in the integer modules is studied in completely new style. By analysis in module and a careful constructing, a condition of non-solution of Diophantine Equation $a^p+b^p=c^q$ is proved that: $(a,b)=(b,c)=1,a,b>0,p,q>12$, $p$ is prime. The proof of this result is mainly in the last two sections.
Category: Number Theory

[404] viXra:1501.0201 [pdf] replaced on 2015-01-28 20:13:35

High Degree Diophantine Equation by Classical Number Theory

Authors: Wu Sheng-Ping
Comments: 6 Pages.

The main idea of this article is simply calculating integer functions in module. The algebraic in the integer modules is studied in completely new style. By analysis in module and a careful constructing, a condition of non-solution of Diophantine Equation $a^p+b^p=c^q$ is proved that: $(a,b)=(b,c)=1,a,b>0,p,q>12$, $p$ is prime. The proof of this result is mainly in the last two sections.
Category: Number Theory

[403] viXra:1501.0201 [pdf] replaced on 2015-01-28 11:18:10

High Degree Diophantine Equation by Classical Number Theory

Authors: Wu Sheng-Ping
Comments: 6 Pages.

The main idea of this article is simply calculating integer functions in module. The algebraic in the integer modules is studied in completely new style. By analysis in module and a careful constructing, a condition of non-solution of Diophantine Equation $a^p+b^p=c^q$ is proved that: $(a,b)=(b,c)=1,a,b>0,p,q>12$, $p$ is prime. The proof of this result is mainly in the last two sections.
Category: Number Theory

[402] viXra:1501.0201 [pdf] replaced on 2015-01-24 05:38:48

High Degree Diophantine Equation by Classical Number Theory

Authors: Wu Sheng-Ping
Comments: 6 Pages.

The main idea of this article is simply calculating integer functions in module. The algebraic in the integer modules is studied in completely new style. By analysis in module and a careful constructing, a condition of non-solution of Diophantine Equation $a^p+b^p=c^q$ is proved that: $(a,b)=(b,c)=1,a,b>0,p,q>12$, $p$ is prime. The proof of this result is mainly in the last two sections.
Category: Number Theory

[401] viXra:1501.0201 [pdf] replaced on 2015-01-23 17:35:12

High Degree Diophantine Equation by Classical Number Theory

Authors: Wu Sheng-Ping
Comments: 6 Pages.

The main idea of this article is simply calculating integer functions in module. The algebraic in the integer modules is studied in completely new style. By analysis in module and a careful constructing, a condition of non-solution of Diophantine Equation $a^p+b^p=c^q$ is proved that: $(a,b)=(b,c)=1,a,b>0,p,q>12$, $p$ is prime. The proof of this result is mainly in the last two sections.
Category: Number Theory