Number Theory

1009 Submissions

[24] viXra:1009.0058 [pdf] submitted on 19 Sep 2010

Infinite Number

Authors: Moon Kyom
Comments: 9 pages

Added the infinite sign and the infinitesimal sign and defined an operation. The infinite calculation of number became possible. The benefits gained by infinite number is as follows.
Category: Number Theory

[23] viXra:1009.0055 [pdf] submitted on 17 Sep 2010

About Goldbach and de Polignac Conjectures

Authors: Jamel Ghanouchi
Comments: 14 pages

(MSC=11) The present algebraic development begins simply by an exposition of the data of the problem. We define the primal radius : For all x an integer greater or equal to 3, we define a primal number r for which x - r and x + r are prime numbers. We see then that Goldbach conjecture would be verified because 2x = (x + r) + (x - r).We prove that the existence of r for all x ≥ 3 can not be proven. We prove also the undecidability of the existence, for all x' an integer, of a primal radius r' for which x'+r' and r'-x' are prime numbers strictly greater than 2. de Polignac conjecture would be quickly verified because 2x' = (x' + r') - (r' - x').
Category: Number Theory

[22] viXra:1009.0054 [pdf] replaced on 17 Nov 2010

An Elementary Proof of Catalan-Mihailescu Theorem

Authors: Jamel Ghanouchi
Comments: 6 pages

( MSC=11D04) More than one century after its formulation by the Belgian mathematician Eugene Catalan, Preda Mihailescu has solved the open problem. But, is it all ? Mihailescu's solution utilizes computation on machines, we propose here not really a proof as it is entended classically, but a resolution of an equation like the resolution of the polynomial equations of third and fourth degrees. This solution is totally algebraic and does not utilize, of course, computers or any kind of calculation.
Category: Number Theory

[21] viXra:1009.0053 [pdf] replaced on 17 Nov 2010

An Approach of Fermat-Catalan Equations

Authors: Jamel Ghanouchi
Comments: 24 pages

We begin with Beal equation (or Fermat-Catalan) Uc+2 = Xa+2 + Yb+2 and establish two equivalent equations. We generalize the approach to all Fermat-Catalan equations which allows us to relate the problem to Matyasevich theorem. Our approach will lead us to propose a new conjecture concerning Fermat-Catalan equations. ( MSC=11D04) Keywords : Fermat-Catalan ; Diophantine equations ; Analysis ; Series ; Fourier series ; Conjecture.
Category: Number Theory

[20] viXra:1009.0049 [pdf] submitted on 14 Sep 2010

The New Prime Theorem (691)-(740)

Authors: Chun-Xuan Jiang
Comments: 70 pages

Using Jiang function we are able to prove almost all prime problems in prime distribution. This is the Book proof. In this paper using Jiang function J2(ω) we prove that the new prime theorems (691)-(740) contain infinitely many prime solutions and no prime solutions.From (6) we are able to find the smallest solution. πk(N0,2) ≥ 1. This is the Book theorem.
Category: Number Theory

[19] viXra:1009.0044 [pdf] submitted on 11 Sep 2010

The New Prime Theorem (641)-(690)

Authors: Chun-Xuan Jiang
Comments: 71 pages

Using Jiang function we are able to prove almost all prime problems in prime distribution. This is the Book proof. In this paper using Jiang function J2(ω) we prove that the new prime theorems (641)-(690) contain infinitely many prime solutions and no prime solutions.From (6) we are able to find the smallest solution. πk(N0,2) ≥ 1. This is the Book theorem.
Category: Number Theory

[18] viXra:1009.0041 [pdf] submitted on 14 Mar 2010

Factoring of the Smarandache Square Product Sequence

Authors: Micha Fleuren
Comments: 4 pages

Factoring of the Smarandache Square Product Sequence
Category: Number Theory

[17] viXra:1009.0040 [pdf] submitted on 14 Mar 2010

Factoring of the Smarandache Prime Product Sequence

Authors: Micha Fleuren
Comments: 6 pages

Factoring of the Smarandache Prime Product Sequence
Category: Number Theory

[16] viXra:1009.0039 [pdf] submitted on 14 Mar 2010

Factoring of the Smarandache Mirror Sequence

Authors: Micha Fleuren
Comments: 4 pages

Factoring of the Smarandache Mirror Sequence
Category: Number Theory

[15] viXra:1009.0038 [pdf] submitted on 14 Mar 2010

Factoring of the Smarandache Factorial Product Sequence

Authors: Micha Fleuren
Comments: 3 pages

Factoring of the Smarandache Factorial Product Sequence
Category: Number Theory

[14] viXra:1009.0037 [pdf] submitted on 14 Mar 2010

Factoring of the Smarandache Back Concatenated Cube Sequence

Authors: Micha Fleuren
Comments: 5 pages

Factoring of the Smarandache Back Concatenated Cube Sequence
Category: Number Theory

[13] viXra:1009.0036 [pdf] submitted on 14 Mar 2010

Factoring of the Smarandache Back Concatenated Even Sequence

Authors: Micha Fleuren
Comments: 6 pages

Factoring of the Smarandache Back Concatenated Even Sequence
Category: Number Theory

[12] viXra:1009.0035 [pdf] submitted on 14 Mar 2010

Factoring of the Smarandache Back Concatenated Odd Sequence

Authors: Micha Fleuren
Comments: 6 pages

Factoring of the Smarandache Back Concatenated Odd Sequence
Category: Number Theory

[11] viXra:1009.0034 [pdf] submitted on 14 Mar 2010

Factoring of the Smarandache Back Concatenated Prime Sequence

Authors: Micha Fleuren
Comments: 5 pages

Factoring of the Smarandache Back Concatenated Prime Sequence
Category: Number Theory

[10] viXra:1009.0033 [pdf] submitted on 14 Mar 2010

Factoring of the Smarandache Back Concatenated Square Sequence

Authors: Micha Fleuren
Comments: 5 pages

Factoring of the Smarandache Back Concatenated Square Sequence
Category: Number Theory

[9] viXra:1009.0032 [pdf] submitted on 14 Mar 2010

Factoring of the Smarandache Concatenated Cubic Sequence

Authors: Micha Fleuren
Comments: 4 pages

Factoring of the Smarandache Concatenated Cubic Sequence
Category: Number Theory

[8] viXra:1009.0031 [pdf] submitted on 14 Mar 2010

Factoring of the Smarandache Concatenated Even Sequence

Authors: Micha Fleuren
Comments: 6 pages

Factoring of the Smarandache Concatenated Even Sequence
Category: Number Theory

[7] viXra:1009.0030 [pdf] submitted on 14 Mar 2010

Factoring of the Smarandache Concatenated Odd Sequence

Authors: Micha Fleuren
Comments: 5 pages

Factoring of the Smarandache Concatenated Odd Sequence
Category: Number Theory

[6] viXra:1009.0029 [pdf] submitted on 14 Mar 2010

Factoring of the Smarandache Concatenated Prime Sequence

Authors: Micha Fleuren
Comments: 4 pages

Factoring of the Smarandache Concatenated Prime Sequence
Category: Number Theory

[5] viXra:1009.0028 [pdf] submitted on 14 Mar 2010

Factoring of the Smarandache Concatenated Square Sequence

Authors: Micha Fleuren
Comments: 4 pages

Factoring of the Smarandache Concatenated Square Sequence
Category: Number Theory

[4] viXra:1009.0027 [pdf] submitted on 14 Mar 2010

Factoring of the Smarandache Cubic Product Sequence

Authors: Micha Fleuren
Comments: 4 pages

Factoring of the Smarandache Cubic Product Sequence
Category: Number Theory

[3] viXra:1009.0026 [pdf] submitted on 14 Mar 2010

Factoring of the Smarandache Deconstructive Sequence

Authors: Micha Fleuren
Comments: 10 pages

Factoring of the Smarandache Deconstructive Sequence
Category: Number Theory

[2] viXra:1009.0021 [pdf] submitted on 7 Sep 2010

The New Prime Theorem (591)-(640)

Authors: Chun-Xuan Jiang
Comments: 70 pages

Using Jiang function we are able to prove almost all prime problems in prime distribution. This is the Book proof. In this paper using Jiang function J2(ω) we prove that the new prime theorems (591)-(640) contain infinitely many prime solutions and no prime solutions.From (6) we are able to find the smallest solution. πk(N0,2) ≥ 1. This is the Book theorem.
Category: Number Theory

[1] viXra:1009.0004 [pdf] submitted on 2 Sep 2010

New Method of Genenating of Primes and Its Application to the Goldbach's Conjecture

Authors: Kunikazu Tanaka
Comments: 21 pages

Showing how to derive new expressions of generating prime numbers to demonstrate the Goldbach's Conjecture
Category: Number Theory