# Number Theory

## 1109 Submissions

[3] **viXra:1109.0054 [pdf]**
*submitted on 27 Sep 2011*

### Expression for the Mathematical Constant e

**Authors:** Ranganath G Kulkarni

**Comments:** 3 pages

Mathematical constant e can be expressed in logarithmic functions. There are six expressions
for e. Five of them are step functions and another one is a constant function.

**Category:** Number Theory

[2] **viXra:1109.0029 [pdf]**
*submitted on 9 Sep 2011*

### Research on Some Smarandache Problems (Vol. 7)

**Authors:** Huaning Liu, Jing Gao

**Comments:** 155 pages

This book systematically introduces the works obtained by using analytic methods on
Smarandache problems. The book includes the basic knowledge of analytic number theory, mean
value on some Smarandache sequences, infinite series involving some Smarandache functions,
hybrid mean value of divisor function and some Smarandache functions, and so on. This book
could open up the reader's perspective, and inspire the reader to these fields.
We want to thank all those who have helped and encouraged us to prepare this book. Professor
Wenpeng Zhang gave us the first impulse for writing this book, and have read the whole manuscript
very carefully. We also thank Yanni Liu and Peng Gao for cover designs. Last but not least,
we would like to thank Dr. Minh Perez for his advice and friendly collaboration.

**Category:** Number Theory

[1] **viXra:1109.0016 [pdf]**
*replaced on 2014-04-19 11:37:27*

### The N-th Root Algorithm

**Authors:** Daniel Cordero Grau

**Comments:** 3 Pages.

In this paper we give the N-th root algorithm in complete normed euclidean semialgebras for every nonzero real N not Newton's approximation by differentials. The algorithm starts with an input semialgebra nonzero element x with arbitrary length n, thereafter writes O(n) semialgebra elements in time O(n) to go through O(n) steps in each of which compares, computes and writes O(1) semialgebra elements in space O(n^2), and so, in time O(n^3).

**Category:** Number Theory