Proving divisibility for $256 \mid 7^{2n} + 208n - 1$ I can't come up with a way of proving this:
$$256 \mid 7^{2n} + 208n - 1\\ \forall n \in \Bbb N$$
I've tried by induction but couldn't see when to apply the inductive hypothesis...
$$P(n+1) = 7^{2n+2}+208n+207$$
How can I continue?
Thank you

By inductive hypothesis $7^{2n}+208n-1=256m$, $m\in \mathbb{N}$
Therefore $7^{2n+2}+208n+207=49(256m+1-208n)+208n+207=49\cdot256m-48\cdot208n+256=49\cdot256m-39\cdot256n+256=256(49m-39n+1)$ is divisible by $256$.
