prove by induction $7 \mid 3^{3^n}+8$ Okay so ive been trying to prove this for about 5 hours... 
really need salvation from the geniouses around here.
prove  by induction
$7\mid 3^{3^n}+8$
i really need some directions on what to do here... 

We have to show that :
$$3^{3^n}+8 \equiv 0 \pmod 7 \Rightarrow 3^{3^n}+1 \equiv 0 \pmod 7$$
$$n=1: 3^{3}+1=3^{2+1}+1=3^2 \cdot 3+1=2 \cdot 3+1=7 \equiv 0 \pmod 7 \checkmark$$
$$\text{We suppose that the relation stands for n: }  \ 3^{3^n}+1 \equiv 0 \pmod 7$$
For $n+1$:
$$ 3^{3^{n+1}}+1=3^{3^n \cdot 3}+1 \equiv (3^{3^n})^3+1 \equiv (-1)^3+1 \equiv -1+1 \equiv 0 \pmod 7$$
