本課程旨在介紹初等數論的基本概念與方法。內容涵蓋整除性、質數、歐幾里得算法、同餘、剩餘類、算術函數、不定方程、二次剩餘以及連分數等主題。課程將兼顧理論理解與解題技巧，培養學生對數論核心思想的掌握，並使學生了解數論在密碼學與計算機科學等領域中的基礎應用。同時，培養學生嚴謹的數學推理能力與證明技巧，建立後續進修抽象代數、代數數論與密碼學的基礎。

This course aims to introduce the basic concepts and methods of elementary number theory. Topics include divisibility, prime numbers, Euclidean arithmetic, congruence, remainder classes, arithmetic functions, indefinite equations, quadratic remainders, and continued fractions. The course will take into account theoretical understanding and problem-solving skills, cultivate students' mastery of the core ideas of number theory, and enable students to understand the basic applications of number theory in fields such as cryptography and computer science. At the same time, students will develop rigorous mathematical reasoning abilities and proof skills, and establish a foundation for subsequent studies in abstract algebra, algebraic number theory, and cryptography.

教科書：
Elementary Number Theory, David M. Burton.
參考書籍：
Elementary Number Theory and Its Applications, Kenneth H. Rosen.

Textbook:
Elementary Number Theory, David M. Burton.
Reference books:
Elementary Number Theory and Its Applications, Kenneth H. Rosen.