Newton polynomials and a class of Diophantine equations

Abstract

The well known result by G. Pólya and G. Szegö upon which if a polynomial of degree n takes integral values for n + 1 consecutive integral values of the variable, then it takes integral values for allintegral values of the variable, is generalized to the case of arbitrarily spaced abscissae, as well as to the case of several variables. An application of such results is then made to certain Diophantine equations, for instance to Pn(x) = y, where Pn denotes the nth degree Newton interpolatory polynomial.