摘要
本文针对在校大学生在学习《初等数论》《竞赛数学》等课程中产生的困惑的基础上,首先介绍一个奇妙的解决困惑的方法——"Euler演段",同时在给出Euler演段概念的基础上,利用辗转相除法结合数学归纳法对"Euler演段"的正确性给予证明;最后给出了该方法在学习《初等数论》《竞赛数学》中如何求最大公约数、最小公倍数、解k元一次不定方程、解一次同余方程等方面的实际应用.
An Euler deduction is introduced as a miracle method to solve the dilemma encountered by the college students in their study of such courses as " Elementary Number Theory" and " Competition Mathematics". After an introduction to the concept of Euler deduction,this paper proves the validity of Euler deduction,employing division algorithm in combination with mathematical induction. It is also applied in the students ' study of above courses to seek greatest common divisor and lowest common multiple,and to solve K ray indefinite equation and congruence equation.
出处
《绵阳师范学院学报》
2017年第11期11-15,48,共6页
Journal of Mianyang Teachers' College
基金
教育部课程教材研究所"十二五"规划重点课题(KC2011-021)
关键词
数论
Euler演段
数学问题
不定方程
同余方程
Number theory,Euler deduction,mathematical problem,indefinite equation,congruence equatio