[7] **viXra:1011.0077 [pdf]**
*replaced on 15 Jan 2011*

**Authors:** Li Zhou

**Comments:** 7 pages.

We discuss the logical fallacies in an article appeared in The
American Mathematical Monthly [6], and present the historical origin
and motivation of the simple proofs of the irrationality of π.

**Category:** Number Theory

[6] **viXra:1011.0047 [pdf]**
*submitted on 21 Mar 2010*

**Authors:** Florentin Smarandache

**Comments:** 98 pages, in Romanian

New functions introduced in number theory by the author are presented, studied,
generalized some of them, and contributions of other mathematicians to these functions
are also showed up.

**Category:** Number Theory

[5] **viXra:1011.0045 [pdf]**
*submitted on 21 Mar 2010*

**Authors:** Florentin Smarandache

**Comments:** 120 pages, in Romanian

Definitions, constructions, properties, and solved and unsolved problems on
Smarandache type functions are presented in this book.

**Category:** Number Theory

[4] **viXra:1011.0031 [pdf]**
*submitted on 20 Mar 2010*

**Authors:** Florentin Smarandache

**Comments:** 1 pages

Demonstration by recurrence on m .

**Category:** Number Theory

[3] **viXra:1011.0030 [pdf]**
*submitted on 20 Mar 2010*

**Authors:** Florentin Smarandache

**Comments:** 1 pages

If p is a real number...

**Category:** Number Theory

[2] **viXra:1011.0029 [pdf]**
*submitted on 20 Mar 2010*

**Authors:** Florentin Smarandache

**Comments:** 2 pages

One generalizes the inequality of Hödler thanks to a reasoning by recurrence. As
particular cases, one obtains a generalization of the inequality of
Cauchy-Buniakovski-Scwartz, and some interesting applications.

**Category:** Number Theory

[1] **viXra:1011.0027 [pdf]**
*submitted on 20 Mar 2010*

**Authors:** Florentin Smarandache

**Comments:** 2 pages

Let us consider the real numbers...

**Category:** Number Theory