Natural numbers are the oldest human invention.

This book describes their nature, laws, history and current status. It has seven chapters. The first five chapters contain not only the basics of elementary number theory for the convenience of teaching and continuity of reading, but also many latest research results.

The first time in history, the traditional name of the Chinese Remainder Theorem is replaced with the Qin Jiushao Theorem in the book to give him full credit for his establishment of this famous theorem in number theory.

Chapters Overview

Chapter 6 is about the fascinating congruence modulo an integer power, and Chapter 7 introduces a new problem extracted by the author from the classical problems of number theory, which is out of the combination of additive number theory and multiplicative number theory.

Features of the Book

One feature of the book is the supplementary material after each section, thereby broadening the reader's knowledge and imagination. These contents either discuss the rudiments of some aspects or introduce new problems or conjectures and their extensions, such as perfect number problem, Egyptian fraction problem, Goldbach's conjecture, the twin prime conjecture, the 3x + 1 problem, Hilbert Waring problem, Euler's conjecture, Fermat's Last Theorem, Landau's problem and others.

This book is written for anyone who loves natural numbers, and it can also be read by mathematics majors, graduate students, and researchers. The book contains many illustrations and tables. Readers can appreciate the author's sensitivity to history, broad range of knowledge, and elegant writing style, while benefiting from the classical works and great achievements of masters in number theory.