Olympiad Number Theory (Mathematics Elevate Olympiad Series)

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 methodsModular arithmetic, residue systems, and the Chinese Remainder TheoremOrders, primitive roots, Fermat/Euler/Wilson theoremsp-adic valuations and the LTE lemma (with contest-friendly templates)Diophantine equations: linear, quadratic, exponential, and Vieta jumpingQuadratic residues, Legendre symbol, and quadratic reciprocity quicksheetArithmetic functions, Möbius inversion, and multiplicativityContinued fractions and Pell’s equations for rational approximation problemsInequalities, extremal number theory, and classical bounding techniquesHensel lifting and polynomial root-lifting in modular arithmeticThis 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 WorldwideTeachers, coaches, and math clubs seeking structured advanced materialAnyone who wants a deep understanding of the beauty and power of number theoryWith 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. Read more