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Explore the fundamental concepts of elementary number theory in this comprehensive lecture delivered in Chinese. Delve into core mathematical principles including divisibility, prime numbers, greatest common divisors, and modular arithmetic through systematic explanations and problem-solving techniques. Master essential theorems such as the Euclidean algorithm, Fermat's Little Theorem, and the Chinese Remainder Theorem while developing analytical skills crucial for advanced mathematical study. Examine practical applications of number theory concepts through worked examples and exercises designed to strengthen computational abilities and theoretical understanding. Build a solid foundation in mathematical reasoning and proof techniques that serve as prerequisites for higher-level mathematics courses in algebra, cryptography, and discrete mathematics.
