Number Theory

1006 Submissions

[7] viXra:1006.0060 [pdf] submitted on 13 Mar 2010

A Method to Solve the Diophantine Equation a X2-B Y2 + C = 0

Authors: Florentin Smarandache
Comments: 10 pages.

We consider the equation (1) ax2 - by2 + c = 0, with a,b ε N* and c ε Z*. It is a generalization of Pell's equation: x2 -Dy2 = 1. Here, we show that: if the equation has an integer solution and a.b is not a perfect square, then (1) has an infinitude of integer solutions; in this case we find a closed expression for (xn,yn), the general positive integer solution, by an original method. More, we generalize it for any Diophantine equation of second degree and with two unknowns.
Category: Number Theory

[6] viXra:1006.0048 [pdf] submitted on 19 Jun 2010

The New Prime Theorem (101)-(130)

Authors: Chun-Xuan Jiang
Comments: 38 pages

Using Jiang function we prove that the new prime theorems (101)-(130) contain infinitely many prime solutions and no prime solutions.
Category: Number Theory

[5] viXra:1006.0047 [pdf] submitted on 19 Jun 2010

The New Prime Theorem (71)-(100)

Authors: Chun-Xuan Jiang
Comments: 38 pages

Using Jiang function we prove that the new prime theorems (71)-(100) contain infinitely many prime solutions and no prime solutions.
Category: Number Theory

[4] viXra:1006.0020 [pdf] submitted on 11 Jun 2010

The New Prime Theorem (141)-(190)

Authors: Chun-Xuan Jiang
Comments: 60 pages

Using Jiang function we prove that the new prime theorems (141)-(190) contain infinitely many prime solutions and no prime solutions.
Category: Number Theory

[3] viXra:1006.0016 [pdf] submitted on 11 Mar 2010

Five Properties of the Smarandache Double Factorial Function

Authors: Felice Russo
Comments: 3 pages

In this paper some properties of the Smarandache double factorial function have been analyzed.
Category: Number Theory

[2] viXra:1006.0014 [pdf] submitted on 11 Mar 2010

About Very Perfect Numbers

Authors: Mihály Bencze, Florin Popovici, Florentin Smarandache
Comments: 3 pages

In this short paper we prove that the square of an odd prime number cannot be a very perfect number.
Category: Number Theory

[1] viXra:1006.0001 [pdf] submitted on 2 Jun 2010

The New Prime Theorem (131)-(140)

Authors: Chun-Xuan Jiang
Comments: 14 pages

Using Jiang function we prove that the new prime theorems (131)-(140) contain infinitely many prime solutions and no prime solutions.
Category: Number Theory