ABSTRACT
A Diophantine equation is a polynomial equation with integer coefficients in which the variables are required to take integer values.
In this chapter, we investigate several types of Diophantine equations, starting with linear equations and progressing to other, more intricate types. In particular, we examine the Pythagorean formula, Pell’s equation, and several equations of Fermat. Along the way, we discover beautiful uses of recurrence relations, mathematical induction (in the guise of the method of descent), and continued fractions. We also investigate Gaussian integers, which are complex numbers that behave much like ordinary integers.
