Diophantine Equations as a Context for Technology-Enhanced Training in Conjecturing and Proving
PRIMUS Volume 18, Number 3, ISSN 1051-1970
Solving indeterminate algebraic equations in integers is a classic topic in the mathematics curricula across grades. At the undergraduate level, the study of solutions of non-linear equations of this kind can be motivated by the use of technology. This article shows how the unity of geometric contextualization and spreadsheet-based amplification of this topic can provide a discovery experience for prospective secondary teachers and information technology students. Such experience can be extended to include a transition from a computationally driven conjecturing to a formal proof based on a number of simple yet useful techniques. (Contains 4 figures.)
Abramovich, S. & Sugden, S.J. (2008). Diophantine Equations as a Context for Technology-Enhanced Training in Conjecturing and Proving. PRIMUS, 18(3), 257-275.