Modular Arithmetic and Primality Testing Fundamentals

Understanding prime numbers and modular arithmetic is essential for modern algorithms, cybersecurity, and computer science. This text-based course guides you step by step through core number theory concepts and efficient computational techniques. What you'll learn: Understand core modular arithmetic operations including modular addition, multiplication, and inverses. Apply the Extended Euclidean Algorithm to solve linear congruences. Compute large powers efficiently using modular exponentiation algorithms. Implement and evaluate probabilistic primality testing techniques like the Miller-Rabin test. Analyze error probabilities and computational complexity in number-theoretic algorithms. Explore practical connections to foundational public-key cryptography and secure communication protocols. The course begins with clear definitions and foundational properties before progressing to algorithmic implementations and practical written exercises. Designed for beginners in programming and mathematics, with no advanced background required. Start reading to strengthen your understanding of computational number theory today.