About Polynomials Whose Divided Differences are Integer-Valued on Prime Numbers

Abstract

We first globalize some recent results about polynomials whose divided differences are integer-valued on subsets of discrete valuation domains. This allows us to describe explicit computations, in particular for polynomials which are integer-valued on the prime numbers. Then, we specialize other recent results about integer-valued polynomials on triangular matrices to matrices whose coefficients are in some subsets, and in particular, when the coefficients are primes.