Abstract: The presence of the number theory in mathematical academic curriculum
is predominantly focused on discussion and validating of strategies for
simplifying calculations with numbers. Beyond this pragmatic aspect, there is
another rich opportunity to work with the number theory in direct connection with the fundamentals of mathematical thinking. In this article, I present definitions
and some properties of happy and polite numbers, which can be a rich
material to work with the arithmetic and algebraic aspects of number theory in
a classroom with upper secondary students.
Key words: number theory, happy numbers, polite numbers, figurate numbers,
mathematical thinking, computer programming.