Foundations of Number Theory with Practical Problem Solving

Unlock the beauty and power of number theory, the branch of mathematics that governs the properties and relationships of numbers. This course is designed to demystify complex concepts and help you build a strong mathematical foundation, whether you are preparing for exams, improving your logical reasoning, or exploring computer science applications. You will transition from basic arithmetic to solving sophisticated numerical puzzles using structured, elegant methods. What you will learn: Understand the core definitions of divisibility, prime numbers, and the Greatest Common Divisor (GCD). Apply fundamental theorems including Fermat's Little Theorem and Euler's Totient Theorem to simplify large calculations. Master modular arithmetic and remainder theorems to solve complex congruence equations. Practice deriving divisibility rules and working with power cycles to find last digits. Explore arithmetic, geometric, and harmonic progressions with clear step-by-step written examples. Learn how modern cryptography relies on number theory principles like prime factorization. This written course begins with essential terminology and foundational definitions before guiding you through step-by-step proofs, practical derivations, and structured problem-solving exercises. This course is perfect for beginners, students, and math enthusiasts who want to build their mathematical thinking from the ground up with no advanced prerequisites. Start your journey into the world of higher arithmetic today.