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

**Authors:** Florentin Smarandache

**Comments:**
10 pages.

We consider the equation
(1) ax^{2} - by^{2} + c = 0, with a,b ε N* and c ε Z*.
It is a generalization of Pell's equation: x^{2} -Dy^{2} = 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 (x_{n},y_{n}),
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*

**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*

**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*

**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*

**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*

**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*

**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