The Square Terms in Lucas Sequences Original Research Article

Let {Un(P, Q)} and {Vn(P, Q)} denote the Lucas sequence and companion Lucas sequence, respectively, with parametersPandQ. For all odd relatively prime values ofPandQsuch thatD=P2−4Qis positive, we determine all indicesnsuch thatUn(P, Q), 2Un(P, Q),Vn(P, Q) or 2Vn(P, Q) is a square. The conditionD>0 assures that the result holds for all such sequences whose terms are positive.