This book contains articles treating some elementary (and somehow unusual) inequalities (both algebraic and geometric), in particular one article that cleverly uses the Cauchy-Schwarz inequality for solving a difficult number theory problem. One can also find in the book topics such as Diophantine equations, the Ramanujan sums, Kronecker’s and Weyl’s density theorems, and the distribution of consecutive integers divisible by their number of divisors. In geometry, the Malfatti problem, Newton’s theorem about circumscriptible quadrilaterals, Napoleon polygons, and equifacial tetrahedra are examined. Cayley’s theorem about the number of spanning trees of the complete graph on n vertices, functional equations, and two articles that start from some old Romanian team selection test problems and get into higher algebra and mathematical analysis complete this book.
Authors
- Titu Andreescu
Subjects
- Mixed Topics
Book Details
- Hardcover: 184 pages
- Publisher: XYZ Press (2023)
- Language: English
- ISBN-13: 979-8-9890528-1-3
