Corrigendum to “Polynomial Cunningham chains” [J. Number Theory 131 (11) (2011) 2100–2106]

A sequence of polynomials f1(x),f2(x),… in Z[x], such that f1(x) has positive leading coefficient, each fi(x) is irreducible in Q[x] and fi(x)=xfi−1(x)+ϵ for all i, is defined to be a polynomial Cunningham chain of the first or second kind, depending on whether ϵ=1 or −1 respectively. If k is the least positive integer such that fk+1(x) is reducible in Q[x], then we say the chain has length k. In the previous article, “Polynomial Cunningham chains”, a proof is given that there exist infinitely many polynomial Cunningham chains of length k of either kind. It is also deduced from this result that there exist infinitely polynomial Cunningham chains of infinite length of either kind. However, the proof contains an error. In this article we give correct proofs of these statements.