国际奥林匹克数学竞赛题与费马小定理

International Mathematical Olympiad and Fermat's Minor Theorem

基于开发智力,引导学生提高数学素质,在国际奥林匹克数学竞赛中展现才华;研究分析了数学竞赛题的科学性、知识性、应用性、启发性、趣味性;指出了科学研究的思路:猜想——论证——形成理论或成果;证明了费马小定理;提出了一系列国际奥林匹克数学竞赛题中关于数的整除性问题,应用费马小定理和牛顿二项式定理进行了论证;找出这类问题的命题规律及解题方法,对应试者有指导意义.

Based on development of intelligence, students are being led to improve their math characters and display their artistic talents in the International Mathematical Olympiad, The features of science, knowledge, application, inspiration and interest of mathematical contest are analyzed. The thinking of scientific research is indicated in the paper, including： guess-proof theory or results; proving Fermat＇s Minor Theorem; putting forward a series of issues about exact divisibility in International Mathematical Olympiad and demonstrating it with Fermat＇s Minor Theorem and Newton Binomial Theorem; finding out the regular pattern of assigning topic of such questions and solutions. This kind of thinking will be helpful and instructive to the examinees.