Note well:

${\displaystyle \begin{array}{cc}\multicolumn{1}{c}{x_1}& =2^2+3^2+6^2\\ \multicolumn{1}{c}{x_2}& =3^2+4^2+{12}^2\\ \multicolumn{1}{c}{x_3}& =4^2+5^2+{20}^2\end{array}}$

Show that $x_n$ is always a perfect square.