Number Theory: Modular Arithmetic

This lecture delves into number theory, focusing on modular arithmetic and its applications. The instructor explains the concept of congruence, the properties of modular operations, and how to manipulate numbers in modular arithmetic. Through examples and proofs, the lecture demonstrates how to simplify calculations using modular reduction and exploit patterns in remainders. The discussion covers the significance of equivalence relations, the behavior of powers in modular arithmetic, and the trick of casting out nines. By the end, students gain a deeper understanding of modular arithmetic and its practical implications.