Un criterio generale di divisibilità di due interi

In the secondary school textbooks some classical divisibility criteria between two integer numbers are considered. These criteria, while showing some common aspects, are very different though in terms of other characteristics. In this paper we state and prove a general divisibility criterion, initially given for two digit divisors, written in binomial decimal form. The criterion is based on the determinant of the coefficient matrix of the binomial form and also on a further algebraic condition. Some examples are provided. Finally some generalizations are considered, in particular some cases in which the additional condition is always true. We give a general characterization of these cases.