In the Little Mathematics Library series we now come to Fundamental Theorem of Arithmetic by L. A. Kaluzhnin.

In this booklet, Prof. Kaluzhnin deals with one of the fundamental propositions of arithmetic of rational whole numbers – the uniqueness of their expansion into prime  multipliers. Having established a conncetion between arithmetic and Gaussian numbers and the question of representing integers as sum of squares, Prof. Kaluzhnin has shown the uniqueness of expansion also holds in the arithmetic of complex (Gaussian) whole numbers.  The author hopes that the booklet will not only be of interest to senior schoolboys but will also be useful for teachers.

The book was translated the Russian by Ram S. Wadhwa and was
first published by Mir in 1979.

PDF | Cover | Bookmarks | OCR | 2.8 MB | 44 pp | 600 dpi

You can get the book here. and here

You can get the Magnet/Torrent links here.

Contents

Introduction 7
1.The Fundamental Theorem of Arithmetic. Proof of the First Part 10
2. Division with Remainder and Greatest Common Divisor (GCD) of Two Numbers. Proof of the Second Part of the Fundamental Theorem 12
3. Algorithm of Euclid and Solution of Linear Diophantine Equations  with Two Unknowns 18
4. Gaussian Numbers and Gaussian Whole Numbers 22
5. Gaussian Prime Numbers and Representation of Rational Whole Numbers as Sum of Two Squares 30
6. Yet Another “Arithmetic” 33
Literature 35