Number Theory Foundations for Competitive Mathematics

Number theory is the bedrock of pure mathematics, cryptography, and computer science, yet many struggle with its abstract proofs and theorems. This text-based course guides you step-by-step from basic divisibility rules to advanced modular arithmetic, equipping you with the problem-solving strategies needed to tackle challenging mathematical questions. What you'll learn: • Understand fundamental divisibility, prime numbers, and the Greatest Common Divisor (GCD) using the Euclidean algorithm. • Apply modular arithmetic concepts to solve complex congruences and systems of linear congruences. • Master key theorems including Fermat's Little Theorem, Euler's Totient Theorem, and the Chinese Remainder Theorem. • Explore arithmetic functions such as the Mobius function, Euler's phi-function, and the sum of divisors. • Practice writing rigorous mathematical proofs for number theoretic propositions. The course begins with essential terminology and foundational definitions before progressing through clear, structured text explanations and targeted practice problems designed to build your mathematical reasoning. Perfect for beginners and students preparing for competitive exams, this course requires no advanced prerequisites. Start reading today to build a powerful foundation in the beauty and logic of numbers.