  In this paper we deal with a non-linear Diophantine equation which arises
from the determinant computation of an integer matrix. We show how to find a
solution, when it exists. We define an equivalence relation and show how the
set of all the solutions can be partitioned in a finite set of equivalence
classes and find a set of solutions, one for each of these classes. We find a
formula to express all the solutions and a formula to compute the cardinality
of the set of fundamental solutions. An algorithm to compute the solutions is
proposed and clarified with some examples.
