Question 4
Let $x_1=603$, $x_2=102$ and
$$x_{n+2}=x_{n+1}+x_n+2\sqrt{x_{n+1}x_n-2}\qquad(n\ge1).$$
Prove: (1) every term is a positive integer; (2) infinitely many terms end in the four decimal digits 2003; (3) no term ends in the four digits 2004.
$$x_{n+2}=x_{n+1}+x_n+2\sqrt{x_{n+1}x_n-2}\qquad(n\ge1).$$
Prove: (1) every term is a positive integer; (2) infinitely many terms end in the four decimal digits 2003; (3) no term ends in the four digits 2004.