The square terms in Lucas sequences

Let {U-n(P,Q)} and {V-n(P,Q)} denote the Lucas sequence and companion Lucas sequence, respectively, with parameters P and Q. For all odd relatively prime values of P and Q such that D = P-2 - 4Q is positive. we determine all indices n such that U-n(P,Q), 2U(n)(P,Q), V-n(P,Q) or 2 V-n(P,Q) is a square. The condition D > 0 assures that the result holds for all such sequences whose terms are positive. (C) 1996 Academic Press, Inc.