Explicit Descriptions of the Solution Sets

The size of a polynomial with integer coefficients is computed by replacing each coefficient by its absolute value and evaluating the resulting polynomial at 2. This chapter investigates Diophantine equations in more than two variables of size 13 and higher. The aim is to describe the set of integer solutions to each equation in the “nicest” possible way. The chapter starts by investigating unrestricted Diophantine equations, and then discussed various restricted families, such as quadratic Diophantine equations, equations with three monomials, and symmetric equations. For each category, the equations are solved in the order of their size, and the smallest unsolved equations are left as open questions.