Modular arithmetic: How to solve $3^{n+1} \equiv 1 \pmod{11}$? Please, I can't solve this equation: 

$$3^{n+1}\equiv 1 \pmod{11}$$

for $n \in \mathbb{N}$.

So what should I do please? Thanks.
$3^5=243=11(22)+1\equiv 1\mod 11$

So if $3^{(n+1)}\equiv 1 \mod 11$ we must have $5|(n+1)$(as $5$ is the smallest integer such that $3^5\equiv 1\mod 5$)
I use Haskell to get :
4,9,14,19,24,29,34,39,44,49,54,59,64,69,74,79,84,89,94,99...


  [n | n &lt;- [0..100], mod (3^(n+1)) 11 == 1]