I am trying to prove that $3^{4n} + 4^{3n+2}$ is divisible by 17.
So far I thought that 17 can be composed of $2^3 + 3^2$ and because $3^{4n}$ is divisble by $3^2$ and $4^{3n+2}$ is divisble by $2^3$, then it would follow that $3^{4n} + 4^{3n+2}$ is a subset of the multiples of 17, and therefore divisble by 17. Am I insane