数学基础课里的中国剩余定理和Lagrange插值公式

The Chinese Remainder Theorem and Lagrange formula in the course of mathematics

中国剩余定理代表了质朴、深刻、有效的插值思想,是中国先贤智慧的结晶,在数学里起着重要的作用.本文中从中国剩余定理的历史记载出发,阐述该定理的意义,给出一种有效的直接解法.作为应用,直接导出Lagrange插值公式.本研究涉及高等代数、初等数论、近世代数等方面的相关知识,在理解中国剩余定理的意义后,可以非常自然地理解这些内容.

The Chinese Remainder Theorem represents a simple,profound,and effective interpolation thought.It is the crystallization of the wisdom of Chinese sages and plays an important role in mathematics.Starting from the historical records of the Chinese Remainder Theorem,we explain the meaning of the theorem and give an effective direct solution.As an application,Lagrange formula is directly derived.This article involves related knowledge of advanced algebra,elementary number theory,modern algebra,etc.After understanding the meaning of the Chinese remainder theorem,one can understand these contents very naturally.