Foundational Number Theory for Math Olympiads and PRMO

Developing a deep, intuitive grasp of how numbers behave is the key to unlocking complex mathematical puzzles. This text-based course guides you through the elegant world of number theory, providing the exact theoretical foundation and problem-solving strategies required for competitive exams like the Pre-Regional Mathematical Olympiad. You will transform from memorizing formulas to logically dissecting and solving intricate mathematical proofs. What you will learn: Understand fundamental concepts of divisibility, prime factorization, and the greatest common divisor; Apply modular arithmetic and congruence properties to solve complex remainder problems; Master classical theorems including Fermat's Little Theorem, Euler's Totient Theorem, and the Chinese Remainder Theorem; Solve Diophantine equations and analyze integer solutions using systematic algebraic methods; Practice structured mathematical reasoning to approach unfamiliar olympiad-style problems. The course begins with core definitions and basic divisibility rules before systematically advancing to modular systems, arithmetic functions, and rigorous proof techniques. This course is designed specifically for beginners and aspiring math competitors with no prior background in advanced number theory. Start building your mathematical problem-solving toolkit today.