17 Lectures on Fermat Numbers. From Number Theory to Geometry
Quoting from the foreword by Alena Šolcová: ‘At the beginning of the third millennium, Fermat’s name is held in great respect throughout the whole mathematical community. This book illustrates how one of Fermat’s famous challenges led to developments in mathematics from number theory to geometry.’ Let us also quote the authors: ‘This book was written on the occasion of the 400th anniversary of Pierre de Fermat’s birth (1601) … We followed an old Chinese proverb that a picture is worth a thousand words.’
The first three chapters of this book deal with basic results on Fermat numbers. In the chapter on ‘The most beautiful theorems on Fermat numbers’, we find theorems of Goldbach, Gauss, Abel, Lucas and Suyama and the crucial result that the fifth Fermat number is divisible by 641. The text covers other aspects of the subject, including open problems and a Euclidean construction of the regular heptadecagon. The reader is required to know only some elementary facts from algebra. This makes the book ideal for a general mathematical audience, students, and researchers from other fields interested in number theory.