On a Kind of Nonlinear Diophantine Equation

In this paper we show a way to generalize the linear Diophantine equation a1x1+a2x2+…+anxn=d . We deal with the nonlinear Diophantine equation det|A X|=±d , which generalizes the linear one, and we give a necessary and sufficient condition for its solvabiliy. We show how the linear equation can be considered as a particular case of the nonlinear equation.