Prove that \(5^{3^n} + 1\) is divisible by \(3^{n + 1}\) for all nonnegative integers \(n\).
Please show all your work.
Just use LTE lemma.
Thanks for responding. I don't know what that is or how to use it. Is there another way to do it?
\(Hint: 5^{3^{k+1}}+1=(5^{3^{k}})^{3}+1=(5^{3^{k}}+1)(5^{2⋅3^{k}}−5^{3^{k}}+1)\)
