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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. 

 Jul 26, 2022
 #1
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Just use LTE lemma.

 Jul 26, 2022
 #2
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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
 #3
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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

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