Lucas sequences whose 12th or 9th term is a square

Let P and Q be non-zero relatively prime integers. The Lucas sequence {Un(P,Q)} is defined byU0=0, U1=1, Un=PUn−1−QUn−2 (n 2).We show that the only sequence with U12(P,Q) a perfect square is the Fibonacci sequence {Un(1,−1)}; and we show that there are no non-degenerate sequences {Un(P,Q)} with U9(P,Q) a perfect square. The argument involves finding all rational points on several curves of genus 2.