Advanced Number Theory for Math Contests

A Structured Journey Through the Most Powerful Ideas in Competition Number Theory

What you’ll learn
Build a strong foundation in modular arithmetic, divisibility, prime structure, and essential theorems used in math contests.
Apply advanced tools—orders, residues, multiplicative functions—to solve Olympiad-level number theory problems.
Develop strategic reasoning to tackle Diophantine equations, congruence systems, and factorization-based problems.
Gain confidence solving national and international contest problems through guided practice and structured exercises.

Requirements
Basic Number Theory is required.

Description
Advanced Number Theory for Math Contests is a complete, rigorous, and beautifully structured course designed for students preparing for high-level mathematics competitions across the world. Number theory is one of the most elegant branches of mathematics, filled with patterns, surprising results, and problems that require creativity and deep reasoning. This course is built to help you understand these ideas in a clear, intuitive, and competition-focused way.The journey begins with essential foundations—divisibility, modular arithmetic, primes, and classical theorems—and gradually progresses to more advanced and powerful tools such as orders and residues, multiplicative functions, Diophantine equations, lifting techniques, and problem-solving strategies used in Olympiad settings. Each concept is explained from first principles, ensuring that you not only know a technique, but also understand why it works.The course is created by Ashish Kashyap, instructor of multiple highly rated Udemy courses including Math Olympiad Masterclass and Olympiad Geometry – A Beautiful Journey. Having trained thousands of students globally through Shishya Learning, and with years of experience preparing students for contests like AMC, AIME, RMO/INMO, USA(J)MO, IMO, and ISI/CMI entrance exams, I bring clarity, structure, and a problem-solver’s mindset to every lesson.This course complements my other Olympiad-focused courses on geometry and problem-solving, allowing motivated students to build a complete contest-mathematics skillset. Whether you want to strengthen your fundamentals or gain mastery over advanced number theory, this course provides a structured, enjoyable, and deeply insightful learning experience.By the end, you will develop the confidence and mathematical maturity required to solve some of the most challenging number theory problems seen in national and international math contests.

Who this course is for
This course is designed for parents of students who are going to write National and International Math Contests and want to improve their Number Theory.

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