On the finiteness of certain Rabinowitsch polynomials II

Let m be a positive integer and f(m)(x) be a polynomial of the form f(m)(x) = x(2) + x - m. We call a polynomial f(m)(x) a Rabinowitsch polynomial if for t = [rootm] and consecutive integers x = x(0), x(0), + 1,..., x(0) + t - 1, \f(x)l is either 1 or prime. In Byeon (J. Number Theory 94 (2002) 177), we showed that there are only finitely many Rabinowitsch polynomials f(m)(x) such that 1 + 4m is square free. In this note, we shall remove the condition that 1 + 4m is square free. (C) 2002 Elsevier Science (USA). All rights reserved.