Number Theory

1011 Submissions

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

On "Discovering and Proving that π is Irrational"

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

On New Functions in Number Theory

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

New Functions in Number Theory

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

A Generalization of an Inequality of Tchebychev

Authors: Florentin Smarandache
Comments: 1 pages

Demonstration by recurrence on m .
Category: Number Theory

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

A Generalization of the Inequality of Minkowski

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

A Generalization of the Inequality of H&oulm;lder

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

A Generalization of the Inequality Cauchybouniakovski-Schwarz

Authors: Florentin Smarandache
Comments: 2 pages

Let us consider the real numbers...
Category: Number Theory