Solving a Diophantine problem using different expressions of the difference of two squares

Abstract

Guided discovery learning can be included in the teaching methods supporting independent and active learning. This paper presents ways how to create and implement guided discovery lessons focused on the investigation of some properties of natural numbers. The subject of divisibility can offer many interesting problems which the teacher may use to develop students' mathematical competencies and the creative thinking. The key elements of the paper are the discovery and proof of the relationship for the sum of the first consecutive odd natural numbers and its application to the investigation of the differences of powers of natural numbers. Numerical and graphical spreadsheet tools are used to increase the students´ interest and speed up calculations in certain stages of learning.