2015/025) Show that $7^{2n} - 48n - 1$ is divisible by 2304

proof:

$7^{2n} - 48n - 1 = 49^n - 48 n - 1 = (1+ 48)^n - 48n - 1$
= $1+ 48n + 48^2{n \choose 2}+ 48^2{n \choose 3}+ \cdots + 48^n - 48n - 1$
=  $48^2{n \choose 2}+ 48^2{n \choose 3}+ \cdots + 48^n$
and as each term is divisible by 48^2 so the value is dvisible by 48^2 or 2304