Uso de la historia de la matemática y la resolución de problemas retadores en la enseñanza y aprendizaje de las ecuaciones diofánticas cuadráticas

Abstract

One of the important topics in the student's mathematical training is the quadratic equation, since in addition to developing algebraic thinking, it has many applications in everyday life. The equations in general, depending on their nature, have solutions that can be integer, rational, real, complex, etc. A special class of quadratic equations, which is generally not taken into account in the mathematics curriculum at the secondary level, are the so called quadratic diophantine equations. One of the interesting characteristics of the study of these equations is that it is not easy to find their solutions and most of the time you must resort to the ingenuity and knowledge belonging to number theory to reach them. In addition, this type of equations is full of history, because many famous mathematicians have dedicated part of their life researching methods to find their solutions.