Олимпиадная теория чисел: продвинутые техники, структуры и решение задач для математических олимпиад

Olympiad Number Theory is a complete, rigorous, and accessible guide to one of the most powerful subjects in problem-solving. Designed for students preparing for BMO, INMO, USAMO, APMO, IMO, Various National Olympiads and college entrance examinations, this book builds number-theoretic mastery from the ground up—starting with divisibility and congruences, and progressing to advanced techniques such as quadratic reciprocity, continued fractions, Hensel lifting, and p-adic valuation methods. Written by Rishabh Kumar, alumnus of IIT Guwahati and Indian Statistical Institute, and an experienced mentor of high-achieving math students, the book blends clarity, depth, and contest insight. Each topic is presented with definitions, fully worked examples, classical strategies, and carefully curated problem sets. Inside this volume, you will find: Divisibility, GCD, LCM, and Euclidean methods Modular arithmetic, residue systems, and the Chinese Remainder Theorem Orders, primitive roots, Fermat/Euler/Wilson theorems p-adic valuations and the LTE lemma (with contest-friendly templates) Diophantine equations: linear, quadratic, exponential, and Vieta jumping Quadratic residues, Legendre symbol, and quadratic reciprocity quicksheet Arithmetic functions, Möbius inversion, and multiplicativity Continued fractions and Pell’s equations for rational approximation problems Inequalities, extremal number theory, and classical bounding techniques Hensel lifting and polynomial root-lifting in modular arithmetic This book is ideal for: Students preparing for Various National & International Olympiads like USAMO, AMC, BMO, SMO, INMO, ... Aspirants of ISI, CMI, and global university exams, Mathematics Contest Worldwide Teachers, coaches, and math clubs seeking structured advanced material Anyone who wants a deep understanding of the beauty and power of number theory With a perfect balance of theory, strategy, and problem practice, Olympiad Number Theory serves both as a textbook and a long-term reference for competitive mathematics.