Find all strings of $w$ that satisfy following equation

Question

Solve the following string equation on the alphabet $A = \{1, 0\}$ and find all $w$'s:

$w011 = 011w$

Answer 1

$w_0$	$w_1$	$w_2$	$w_3$	$w_4$	...	$w_{n-2}$	$w_{n-1}$	$w_{n}$	0	1	1
0	1	1	$w_0$	$w_1$	...	$w_{n-5}$	$w_{n-4}$	$w_{n-3}$	$w_{n-2}$	$w_{n-1}$	$w_{n}$

We can see that $w_0$ has to be equal to $w_3$, $w_6$... Recursively $n-2$ has to be divisible by 3, because only $w_0 = 0$ from set {$w_0$, $w_1$, $w_2$}. So all strings are of form $(011)*$.

So we have $w=\emptyset$, $w = 011$, $w=011011$...