On the Solutions of det(A/X)=+-d
arXiv:1707.07629
Abstract
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.
31 pages