Number Theory for JEE and Competitive Mathematics

Number theory is the backbone of advanced algebra and competitive mathematics, yet many students struggle to move beyond basic arithmetic to solve complex exam problems. This text-only course provides a structured, step-by-step approach to mastering the core principles of number theory required for competitive exams. You will transition from memorizing formulas to deeply understanding the properties of integers, prime numbers, and modular systems. By reading clear explanations and studying solved mathematical proofs, you will develop the analytical skills needed to tackle non-routine algebraic challenges. What you'll learn: - Understand fundamental divisibility rules, prime factorization, and the Euclidean algorithm. - Apply modular arithmetic and congruences to solve complex remainder problems. - Master Euler's totient function, Fermat's Little Theorem, and Wilson's Theorem. - Solve linear congruences and explore the Chinese Remainder Theorem. - Practice identifying and applying number-theoretic functions in algebraic equations. - Explore modern applications of number theory, including basic algorithmic efficiency and cryptography concepts. The course begins with foundational definitions of divisibility and prime properties before advancing to modular systems, residue classes, and advanced theorems. Each section pairs theoretical explanations with written walkthroughs of exam-style problems to build your confidence. Designed for students preparing for competitive exams like the JEE, math olympiad aspirants, and anyone seeking a solid foundation in discrete mathematics. Start reading today to unlock the elegant patterns of numbers and elevate your mathematical problem-solving skills.