Number Theory

1005 Submissions

[36] viXra:1005.0107 [pdf] submitted on 11 Mar 2010

On the Mean Value of the Additive Analogue of Smarandache Function

Authors: Yi Yuan, Zhang Wenpeng
Comments: 3 pages

see paper for abstract
Category: Number Theory

[35] viXra:1005.0106 [pdf] submitted on 11 Mar 2010

An Introduction to the Smarandache Square Complementary Function

Authors: Felice Russo
Comments: 13 pages

In this paper the main properties of Smarandache Square Complementary function has been analyzed. Several problems still unsolved are reported too.
Category: Number Theory

[34] viXra:1005.0105 [pdf] submitted on 11 Mar 2010

Some New Results Concerning the Smarandache Ceil Function

Authors: Sabin Tabirca, Tatiana Tabirca
Comments: 7 pages

In this article we present two new results concerning the Smarandache Ceil function. The first result proposes an equation for the number of fixed-point number of the Smarandache ceil function. Based on this result we prove that the average of the Smarandache ceil function is Θ(n) .
Category: Number Theory

[33] viXra:1005.0102 [pdf] replaced on 19 Jun 2010

The New Prime Theorem (45)-(70)

Authors: Chun-Xuan Jiang
Comments: 33 pages

Using Jiang function we prove that the new prime theorems (45)-(70) contain infinitely many prime solutions and no prime solutions.
Category: Number Theory

[32] viXra:1005.0096 [pdf] submitted on 24 May 2010

The Sieve Method of the Number of Solutions of Goldbach Conjecture (A)

Authors: Tong Xin Ping
Comments: 3 Pages, In Chinese

We can find all solutions of Goldbach conjecture (A) ling in the closed interval [pr+1, N-pr-1], and we can obtain expression of the number of solutions of Goldbach conjecture (A).
Category: Number Theory

[31] viXra:1005.0092 [pdf] submitted on 11 Mar 2010

Seven Conjectures in Geometry and Number Theory

Authors: Florentin Smarandache
Comments: 2 pages

In this short paper we propose four conjectures in synthetic geometry that generalize Erdos-Mordell Theorem, and three conjectures in number theory that generalize Fermat Numbers.
Category: Number Theory

[30] viXra:1005.0088 [pdf] submitted on 21 May 2010

The New Prime Theorem (44)

Authors: Chun-Xuan Jiang
Comments: 2 pages

Using Jiang function J2(ω) we prove that jPn + 9 - j contain infinitely many prime solutions.
Category: Number Theory

[29] viXra:1005.0087 [pdf] submitted on 21 May 2010

The New Prime Theorem (43)

Authors: Chun-Xuan Jiang
Comments: 3 pages

Using Jiang function we prove that jP8 + k - j contain infinitely many prime solutions.
Category: Number Theory

[28] viXra:1005.0086 [pdf] submitted on 21 May 2010

The New Prime Theorem (42)

Authors: Chun-Xuan Jiang
Comments: 3 pages

Using Jiang function we prove that jP7 + k - j contain infinitely many prime solutions.
Category: Number Theory

[27] viXra:1005.0085 [pdf] submitted on 21 May 2010

The New Prime Theorem (41)

Authors: Chun-Xuan Jiang
Comments: 3 pages

Using Jiang function we prove that jP6 + k - j contain infinitely many prime solutions.
Category: Number Theory

[26] viXra:1005.0084 [pdf] submitted on 21 May 2010

The New Prime Theorem (40)

Authors: Chun-Xuan Jiang
Comments: 3 pages

Using Jiang function we prove that jP5 + k - j contain infinitely many prime solutions.
Category: Number Theory

[25] viXra:1005.0083 [pdf] submitted on 21 May 2010

The New Prime Theorem (39)

Authors: Chun-Xuan Jiang
Comments: 3 pages

Using Jiang function we prove that if J2(ω) ≠ 0 then there are infinitely many primes P such that each of jP4 + k - j is a prime, J2(ω) = 0 then there are finite primes P such that each of jP4 + k - j is a prime.
Category: Number Theory

[24] viXra:1005.0067 [pdf] submitted on 11 Mar 2010

The Smarandache P and S Persistence of a Prime

Authors: Felice Russo
Comments: 5 pages.

The Smarandache P and S persistence of a prime
Category: Number Theory

[23] viXra:1005.0064 [pdf] submitted on 15 May 2010

Santilli's Isoprime Theory

Authors: Chun-Xuan Jiang
Comments: 16 Pages

We establish the Santilli's isomathematics based on the generalization of the modern mathematics. (see paper for rest of abstract with equations)
Category: Number Theory

[22] viXra:1005.0058 [pdf] submitted on 11 Mar 2010

Partition of a Set which Contains an Infinite Arithmetic (Respectively Geometric) Progression

Authors: Florentin Smarandache
Comments: 3 pages

We prove that for any partition of a set which contains an infinite arithmetic (respectively geometric) progression into two subsets, at least one of these subsets contains an infinite number of triplets such that each triplet is an arithmetic (respectively geometric) progression.
Category: Number Theory

[21] viXra:1005.0054 [pdf] submitted on 11 Mar 2010

Some Smarandache Problems

Authors: Mladen V. Vassilev-Missana, Krassimir T. Atanassov
Comments: 67 pages, Book in Romanian, French and English. Proposed and solved problems for students' mathematical competitions in number theory, algebra, geometry, trigonometry, calculus.

During the five years since publishing [2], we have obtained many new results related to the Smarandache problems. We are happy to have the opportunity to present them in this book for the enjoyment of a wider audience of readers. The problems in Chapter two have also been solved and published separately by the authors, but it makes sense to collate them here so that they can be better seen in perspective as a whole, particularly in relation to the problems elucidated in Chapter one. Many of the problems, and more especially the techniques employed in their solution, have wider applicability than just the Smarandache problems, and so they should be of more general interest to other mathematicians, particularly both professional and amateur number theorists.
Category: Number Theory

[20] viXra:1005.0049 [pdf] submitted on 11 Mar 2010

Only Problems Not Solutions

Authors: Florentin Smarandache
Comments: 112 pages

The development of mathematics continues in a rapid rhythm, some unsolved problems are elucidated and simultaneously new open problems to be solved appear.
Category: Number Theory

[19] viXra:1005.0047 [pdf] submitted on 11 Mar 2010

A Method of Solving Certain Nonlinear Diophantine Equations

Authors: Florentin Smarandache
Comments: 2 pages

In this paper we propose a method of solving a Nonlinear Diophantine Equation by converting it into a System of Diophantine Linear Equations.
Category: Number Theory

[18] viXra:1005.0042 [pdf] submitted on 11 May 2010

New Prime K-Tuple Theorem (20)

Authors: Chun-Xuan Jiang
Comments: 2 Pages

Using Jiang function we prove for any there are infinitely many primes P such that each of jPP0 + j+1 is a prime.
Category: Number Theory

[17] viXra:1005.0041 [pdf] submitted on 11 May 2010

New Prime K-Tuple Theorem (19)

Authors: Chun-Xuan Jiang
Comments: 2 Pages

Using Jiang function we prove for any there are infinitely many primes P such that each of PP0 + 4n is a prime.
Category: Number Theory

[16] viXra:1005.0040 [pdf] submitted on 11 May 2010

New Prime K-Tuple Theorem (18)

Authors: Chun-Xuan Jiang
Comments: 2 Pages

Using Jiang function we prove for any there are infinitely many primes kPsuch that each of PP0 + (2j)2 is a prime.
Category: Number Theory

[15] viXra:1005.0039 [pdf] submitted on 11 May 2010

New Prime K-Tuple Theorem (17)

Authors: Chun-Xuan Jiang
Comments: 2 Pages

Using Jiang function we prove for any there are infinitely many primes kPsuch that each of PP0 + j(j+1) is a prime.
Category: Number Theory

[14] viXra:1005.0038 [pdf] submitted on 11 May 2010

New Prime K-Tuple Theorem (16)

Authors: Chun-Xuan Jiang
Comments: 2 Pages

Using Jiang function we prove for any k there are infinitely many primes P such that each of jP5 + j +1 is a prime.
Category: Number Theory

[13] viXra:1005.0037 [pdf] submitted on 11 May 2010

New Prime K-Tuple Theorem (15)

Authors: Chun-Xuan Jiang
Comments: 2 Pages

Using Jiang function we prove for any k there are infinitely many primes P such that each of P5 + 4n is a prime.
Category: Number Theory

[12] viXra:1005.0036 [pdf] submitted on 11 May 2010

New Prime K-Tuple Theorem (14)

Authors: Chun-Xuan Jiang
Comments: 2 Pages

Using Jiang function we prove for any k there are infinitely many primes P such that each of P5 + (2j)2 is a prime.
Category: Number Theory

[11] viXra:1005.0035 [pdf] submitted on 11 May 2010

New Prime K-Tuple Theorem (13)

Authors: Chun-Xuan Jiang
Comments: 2 Pages

Using Jiang function we prove for any k there are infinitely many primes P such that each of P5 + j( j +1) is a prime.
Category: Number Theory

[10] viXra:1005.0032 [pdf] submitted on 9 May 2010

New Prime K-Tuple Theorem (12)

Authors: Chun-Xuan Jiang
Comments: 2 Pages

Using Jiang function we prove for any k there are infinitely many primes P such that each of jP3 + j + 1 is a prime.
Category: Number Theory

[9] viXra:1005.0031 [pdf] submitted on 9 May 2010

New Prime K-Tuple Theorem (11)

Authors: Chun-Xuan Jiang
Comments: 2 Pages

Using Jiang function we prove for any k there are infinitely many primes P such that each of P3 + 4n is a prime.
Category: Number Theory

[8] viXra:1005.0030 [pdf] submitted on 9 May 2010

New Prime K-Tuple Theorem (10)

Authors: Chun-Xuan Jiang
Comments: 2 Pages

Using Jiang function we prove for any k there are infinitely many primes P such that each of P3 + (2 j)2 is a prime.
Category: Number Theory

[7] viXra:1005.0029 [pdf] submitted on 9 May 2010

New Prime K-Tuple Theorem (9)

Authors: Chun-Xuan Jiang
Comments: 2 Pages

Using Jiang function we prove that P, P15 + j(j+1)(j=1,...,7) contain no prime solutions.
Category: Number Theory

[6] viXra:1005.0028 [pdf] submitted on 9 May 2010

New Prime K-Tuple Theorem (8)

Authors: Chun-Xuan Jiang
Comments: 2 Pages

Using Jiang function we prove that P, P9 + j(j+1)(j=1,...,7) contain no prime solutions.
Category: Number Theory

[5] viXra:1005.0027 [pdf] submitted on 9 May 2010

New Prime K-Tuple Theorem (7)

Authors: Chun-Xuan Jiang
Comments: 2 Pages

Using Jiang function we prove for any k there are infinitely many primes P such that each of P3 + j( j + 1) is a prime.
Category: Number Theory

[4] viXra:1005.0025 [pdf] submitted on 10 May 2010

Proof of the 3n+1 Problem for N ≥ 1

Authors: Steffen Bode
Comments: 6 Pages.

I establish the existence of a unique binary pattern inherent to the 3n+1 step, and then use this binary pattern to prove the 3n+1 problem for all positive integers.
Category: Number Theory

[3] viXra:1005.0023 [pdf] submitted on 11 Mar 2010

Considerations on New Functions in Number Theory

Authors: Florentin Smarandache
Comments: 20 pages

In this paper a small survey is presented on eighteen new functions and four new sequences, such as: Inferior/Superior f-Part, Fractional f-Part, Complementary function with respect with another function, S-Multiplicative, Primitive Function, Double Factorial Function, S-Prime and S-Coprime Functions, Smallest Power Function.
Category: Number Theory

[2] viXra:1005.0017 [pdf] submitted on 5 May 2010

About an Identity and Its Applications

Authors: Mihály Bencze, Florentin Smarandache
Comments: 2 pages

About an Identity and its Applications
Category: Number Theory

[1] viXra:1005.0008 [pdf] submitted on 2 May 2010

The Improved of the Chen Jing Run Theorem

Authors: Tong Xin Ping
Comments: 3 Pages, In Chinese

Chen Jing Run proved that "On the representation of a large even integer as the sum of a prime and the product of at most two primes" and lower bound estimations of the number of solutions. Jiang Chun Xuan, Tong Xin Ping proved that "An even integer as the sum of a prime and the product of two primes" and compute formula of the number of solutions. This paper compares the accuracy of the three formulas
Category: Number Theory