Lucas sequences whose nth term is a square or an almost square

A. Bremner N. Tzanakis

(Below, \Box means "perfect square") Let $P$ and $Q$ be non-zero integers. The Lucas sequence $\{U_n(P,Q)\}$ is defined by $U_0=0$, $U_1=1$, $U_n=P{U}_{n-1}-Q{U}_{n-2}$, $(n\ge 2)$…