Multiply Integer-Valued Polynomials in a Galois Field

TLDR: In this paper, conditions for a polynomial which together with its higher derivatives are integer-valued are derived for the elements from the ring of polynomials over a Galois field.

Abstract: Consider the elements from the ring ) (x q F of polynomials over a Galois field q F as integers. A polynomial ) (T f over ) (x q F is said to be integer-valued if ) (T f takes values in ) (x q F for all T in . ) (x q F We derive conditions for a polynomial which together with its higher derivatives are integer-valued.