Maple as a tool for the teaching of cyclotomic polynomials elementarily

Zahedi Zahedi, Anton Abdulbasah Kamil, Fajriana Fajriana, Siswadi Siswadi, Almira Almi and, Sarmin Suparni

Cyclotomic polynomials are an interesting topic and play an important role for other topics in Number Theory. For special values of $n$, computing a cyclotomic polynomial is not difficult; this can be done by using properties of the polynomial. For a prime value of $n$, the polynomial can be written quickly. However, for values which are multiples of odd prime numbers, say $85=17\cdot5$, the task can be quite difficult if it must be done manually. The polynomial has 41 terms and the degree of 64. Software for cyclotomic polynomials is available; Maple for example, can solve the problem of cyclotomic polynomials very easily. How\-ever, understanding of how to compute polynomials is very important for a student in applying various properties of the cyclotomic polynomial. Here, we will use Maple to help students understand cyclotomic polynomials from the basic. Answer is not obtained directly but step-by-step using properties of the polynomial. So, Maple is used to simulate the process of obtaining the polynomial. Once the students grasp the skill, they will be able to use the software for advanced applications.