Proof

Question

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272

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Prove that $5^{3^n} + 1$ is divisible by $3^{n + 1}$ for all nonnegative integers $n$ .

Please show all your work.

Guest Jul 26, 2022

Guest · Answer 1 · 2022-07-26T09:57:04

-1

Just use LTE lemma.

Guest Jul 26, 2022

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Thanks for responding. I don't know what that is or how to use it. Is there another way to do it?

Guest Jul 26, 2022

+52

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$Hint: 5^{3^{k+1}}+1=(5^{3^{k}})^{3}+1=(5^{3^{k}}+1)(5^{2⋅3^{k}}−5^{3^{k}}+1)$

Limpeklimpe Jul 27, 2022