Solving Factorial Problems in Number Theory

Factorials are central to number theory, combinatorics, and competitive mathematics, yet solving factorial equations often requires specific analytical strategies. This course provides a clear step-by-step framework for tackling number theory problems involving factorials through written explanations and guided mathematical reasoning. By working through foundational concepts and structured problem-solving patterns, you will build confidence in analyzing prime distributions, trailing zeros, and divisibility properties. What you'll learn: - Understand core properties of factorials and key definitions in number theory - Apply Legendre's formula to determine prime exponents in factorial expansions - Analyze divisibility rules, modular congruences, and Wilson's theorem - Solve Diophantine equations involving factorials using bounding techniques - Evaluate trailing zeros and digit patterns in large factorials systematically - Practice strategic algebraic manipulations for discrete mathematics problems The course begins with fundamental definitions and basic multiplicative properties before advancing into specialized algebraic techniques and Diophantine analysis. It is designed for students, math enthusiasts, and beginners looking to strengthen their discrete math foundation without complex prerequisites. Start reading today to master factorial problem-solving methods.