This article deals with Newton divided difference interpolation polynomials. Textbooks in numerical mathematics where such polynomials are studied usually put the emphasis on numerical problems which are solved using these polynomials. Here we show that such polynomials can also be useful in solving some algebraic problems. In order to present this concept we shall first define the divided differences in the new sense: the divided difference of order $n$ is considered as a function of one variable and $n$ parameters. After the concise presentation of the theory of divided differences, we shall solve the problem of interpolation by integer polynomials. At the end we give the solution of an interesting problem using this theory.