Number Theory for Competitive Programming

Solving algorithmic challenges often requires more than just clean code—it demands a deep understanding of the mathematical foundations that optimize computation. This text-only course guides you from foundational arithmetic concepts to the core number-theoretic algorithms used in top-tier coding competitions. You will learn to identify mathematical patterns and translate them into highly optimized code. What you'll learn: - Understand core divisibility rules, prime factorization, and greatest common divisor algorithms. - Apply modular arithmetic, modular inverses, and Fermat's Little Theorem to prevent integer overflow. - Implement efficient prime-finding techniques, including the Sieve of Eratosthenes and its modern optimized variations. - Solve complex system congruences using the Chinese Remainder Theorem. - Practice translating mathematical proofs into clean, efficient code snippets ready for competitive environments. The course begins with fundamental definitions of divisibility and prime numbers before progressing to modular structures, logarithmic exponentiation, and practical competitive programming templates. Designed for beginners to competitive programming and computer science students, this course requires no advanced mathematical background. Start reading today to unlock the mathematical principles behind high-performance algorithms.