Abstract 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.
