國中數學教師甄試-數論試題之研究

本篇論文主要對國中教師甄試題目，針對數論題目加以研究及探討。高斯曾說：「數學是科學的皇后，數論是數學的皇后。」數論題目千百種，我們將題目分類成幾個主題來討論，費馬小定理、同餘、因式分解、最大公因數及最小公倍數、整數性質等。在此研究過程中，數論題目並不像我們想像中的困難，解法也有其脈絡可循，而研究此論文，讓我對數論題目不再無所適從，而有一定的思維模式，所以也讓我在往後教學教導學生解題時，提供了不少的思考模式來教導。

關鍵字

費馬小定理；數學教師甄試；數論

並列摘要

The study scope of this thesis is to discuss the number theory which is designed as test questions in the qualified/certified exam for junior high school teachers. Johann Carl Friedrich Gau (Gauss) once said,“Mathematics is the Queen of Sciences, and Arithmetic the Queen of athematics.” There are hundreds of question types of the number theory. In this study, questions are divided into several categories which are as follows: Fermat’s little theorem, congruence, factorization, the greatest common divisor, the least common multiple, the properties of integer, etc. In the study process, I found out that questions of the number theory are not difficult as what we imaged at first. The ways of answering questions can be traced back to the thread of thought. After studies, I am not confused about questions of the number theory. I learned there is some certain logical thinking in them. This helps me to provide students with multiple logical thinking hereafter in order to answer questions.