Q:

Prove by induction that $7^{2n}-48n-1$ is divisible by 2304

$$P(n):2304\mid7^{2n}-48n-1$$
I've done the base case; $P(1)$ is true because the expression then evaluates to zero, which is divisible by 2304. Now I'm stuck on the inductive step: proving $P(m+1)$ true if $P(m)$ is true. I do know this though:
$$7^{2m+2}-48(m+1)-1
=49\cdot7^{2m}-48m-49$$

A:

$$7^{2(m+1)} - 48(m+1) - 1 = 49 \cdot 7^{2m} - 48m - 49 = 49\left(7^{2m} - 48m - 1\right) + 2304m$$

