ILL 1976 Problem 14

A sequence $\{ u_n \}$ of integers is defined by $$u_1 = 2, u_2 = u_3 = 7,$$ $$u_{n+1} = u_nu_{n-1} - u_{n-2}, \text{ for }n \geq 3$$ Prove that for each $n \geq 1$ , $u_n$ differs by $2$ from an integral square.