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 a full credit for his establishment of this famous theorem in number theory. 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.

One feature of the book is the supplementary material after each section, there by 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, Laudau's problem and etc.

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 of history, broad range of knowledge, and elegant writing style, while benefiting from the classical works and great achievements of masters in number theory.

�ber die Autorin bzw. den Autor

Tianxin Cai received his PhD in number theory from Shandong University. He is a distinguished professor of mathematics at Zhejiang University as well as a well-known poet, writer, translator and photographer. He has published dozens of books including Numbers and Roses, The Brief History of Mathematics, The Mathematical Stories, Number Theory: from viewpoint of congruence. He also published several memories based on his visiting or travel in USA, UK, Germany, France, Latin America, respectively, and of his childhood and university life by major publishers in China. His poems have been translated into more than 20 languages, with 18 books in 10 languages including two of his selected poems in English, Song of the Quiet Life in Durban, South Africa, Every Cloud has its Own Name in San Francisco, USA. Cai reads his poems widely throughout the world. He also delivered lectures on mathematics and arts in English in dozens of countries. His book of essays Mathematical Legends won the National Award of Science and Technology in 2018. He won Naji Naaman poetry award in Beirut in 2013 and Kathak poetry award in Dakar in 2019.

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