Congruence as an extension to parity

Abstract

Parity (even and odd) is a feature often utilised in solving a mathematical problem. In Pólya’s problem solving model, the solver is encouraged to look back at the solution and pose suitable extensions. Keeping parity as the focus, nice extensions can be posed. In this paper, we give two examples in which seeing parity as a special case of congruence (i.e., as modulo 2) leads to ‘nicer’ extensions.