选择特殊的数为模的解题方法——初等数论在数学竞赛中的应用之一

On the Method of Choosing Certain Moduli——An Application of Elementary Number Theory to Mathematical Competitions

与初等数论知识有关的命题,是数学竞赛,特别是IMO的重要组成部分。选择某些正整数为模,然后运用同余关系进行解题的方法,是参赛者必须掌握的方法。本文介绍在竞赛中如何选择恰当的数为模,并使用同余式的一些基本原则和技巧。

Mathematical competitions, especically IMO, have many problems which assume the knowledge of elementary number theory, It is essentical for the competitors to master the method with which they are able to choose certainnumbres as moduli, then, on applications of congruence relations, to solve the problems. In this paper, we give some basic principles and skills in the choice of appropriate moduli and the application of the Consequent congruence expressions.