The second volume, Book 2, of Introduction to Number Theory in Mathematics Contests starts with focusing on the most important classical, basically polynomial congruences, and arithmetic functions. It features beautiful problems with unique and interesting results, such as the Erd˝os-GinzburgZiv theorem (stating that among any 2n – 1 integers one can find n whose sum is divisible by n), and also some other classical results arising from the Prime Number Theorem. The important (because of its many applications) ”lifting the exponent” lemma is present in the book as well along with the beautiful theorem of Lucas about binomial coefficients modulo a prime, Lagrange’s theorem on the number of solutions of a polynomial congruence modulo a prime, and Gauss’s theorem about the existence/non-existence of primitive roots modulo an arbitrary positive integer.
This book is a great resource for those who have basic mathematics knowledge, especially in Algebra, and want to learn more about fundamental concepts in Number Theory. Students wishing to participate in math competitions as well as those looking to learn more about the beauty of mathematics will benefit the most by having this book on their shelves.Authors
- Titu Andreescu and Marian Tetiva
Subjects
- Number Theory and Combinatorics
Book Details
- Hardcover: 239 pages
- Publisher: XYZ Press (2024)
- Language: English
- ISBN-13: 979-8-9890528-6-8
