Grade 10

Sixty-four every time

A power term plus a linear term is a multiple of 64 for every n. The trick is noticing 49 sits one away from 48 -- the binomial theorem finishes it in one line.

Divisibility
Contest problems

1
Prove it
Prove that for every positive integer $n$ , $7^{2n} + 16n - 1$ is divisible by $64$ .