摘要：中学数学竞赛目的在于激发青少年对数学的兴趣，培养数学探索能力，提高人才的数学素质，以适应未来发展的需要。数学竞赛与中小学素质教育相结合，内容与课堂教学内容协调一致，富于新、奇、巧、趣的创意，渗透现代数学思想和方法，巧用带余除法可以方便地解决中学数学竞赛中的有关问题,可以从国际国内数学竞赛题的设计上得到启示。本文从带余除法定理及其性质出发，列举了带余除法在数学竞赛中的若干典型应用。

关键词：带余除法; 数学竞赛; 中学; 应用;

Abstract：The goal of middle-school mathematics competition is to stimulate teenager’s interest in mathematics, foster their ability of math exploration and develop talents’ quality to adapt to the demands of the development of future. Mathematics Competition combines with ability--oriented education of elementary and secondary school and coordinates with the content of teaching in class, which is full of novel, peculiar, ingenious and interesting originality and permeates modern math thought and methods. Skillfully using division algorithm can easily work out relevant issues in the middle school mathematics competition. We can get inspiration from the design of domestic and international mathematics competition problems. This essay lists some typical applications of division with remainder in the mathematics competition from its theorem and properties. 

Key words:  Division with Remainder; Mathematics Competition; Middle School; Application