Abstract:

Number theory is one of the topics in high school mathematics that requires relatively little prior knowledge. Tasks and problems related to divisibility can be dealt with in high school classes - regardless of age, since students are already introduced to (basic) concepts such as prime numbers, multiples, divisors, or even the basics of number theory - which is further studied as part of university curricula. This knowledge is already sufficient to examine tasks and problems at high school level that are related to the number of dividers. Even in a textbooks designed for upper grade elementary school students, we can come across curiosities like perfect and friendly numbers, or just divisors of square numbers. Although students encounter specific arithmetical functions for the first time mostly at universities, there are already types of tasks in secondary schools that have exactly the same results as the outputs of these types of arithmetical functions, for example: take the sum of the divisors of a particular number. To check and easily understand these types of tasks, we have created a software that serves as a calculator on the one hand and models these functions on the other hand. Graphic outputs are represented by timed simulation or even instantaneous results. The aim of this work is to facilitate the teaching of a few selected arithmetical functions using software that provides graphical outputs. Furthermore, the study assesses the application possibilities of the software at both high school and university education levels, describing the types of functions we have algorithmized (divisor sums function, Euler function, Möbius function) and the types of tasks in which the program can be applied at different levels of public education.

Keywords:

Number theory, arithmetical functions, visualization, application, digitization, apps for education, technology-enhanced learning.