Can someone help me prove that 2^3^n + 1 is divisible by 3^(n+1)??!!

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- Dec 12th 2012, 03:48 AMwille13Have no idea on how to prove
Can someone help me prove that 2^3^n + 1 is divisible by 3^(n+1)??!!

- Dec 12th 2012, 04:28 AMskeeterRe: Have no idea on how to prove
you've not performed induction before?

for $\displaystyle n = 1$ , $\displaystyle 2^{3^n} + 1 = 9$ , $\displaystyle 3^{n+1} = 9$ ... true for $\displaystyle n = 1$

assume true for $\displaystyle n$ , prove true for $\displaystyle n+1$ ...

$\displaystyle 2^{3^{n+1}} + 1 = 2^{3^n \cdot 3} + 1 = (2^{3n})^3 + 1$

the last expression is the sum of two cubes and will factor. can you finish?