On the Finiteness of Certain Rabinowitsch Polynomials Original Research Article

Let m be a positive integer and fm(x) be a polynomial of the form fm(x)=x2+x−m. We call a polynomial fm(x) a Rabinowitsch polynomial if for t=[image] and consecutive integers x=x0, x0+1, …, x0+t−1, f(x) is either 1 or prime. In this note, we show that there are only finitely many Rabinowitsch polynomials fm(x) such that 1+4m is square free.