# Math Help - Have no idea on how to prove

1. ## Have no idea on how to prove

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

2. ## Re: Have no idea on how to prove

you've not performed induction before?

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

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

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

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