On the finiteness of certain Rabinowitsch polynomials II

Let <f>m</f> be a positive integer and <f>fm(x)</f> be a polynomial of the form <f>fm(x)=x2+x−m</f>. We call a polynomial <f>fm(x)</f> a Rabinowitsch polynomial if for <f>t=[√ of <RCD>m</RCD>]</f> and consecutive integers <f>x=x0, x0+1,…,x0+t−1, | f(x)|</f> is either 1 or prime. In Byeon (J. Number Theory 94 (2002) 177), we showed that there are only finitely many Rabinowitsch polynomials <f>fm(x)</f> such that <f>1+4m</f> is square free. In this note, we shall remove the condition that <f>1+4m</f> is square free. [Copyright &y& Elsevier]