Prove by induction that for all natural numbers $n$, $\frac{5}{4}8^n + 3^{3n-1}$ is divisible by $19$.
I'm running into trouble at the inductive part of the step, I am currently attempting to add/subtract the inductive hypothesis but I end up with two different coefficients that are seemingly unrelated to $19$. I've been stuck on this for days, thanks for the help!
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