Explicit Solutions to Small Equations

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 studies Diophantine equations of the smallest size, using elementary methods, such as polynomial factorization, analysis of real solutions, analysis modulo m, methods for linear equations and equations with two monomials. It shows that these methods suffice to solve all equations of size up to 8.