134. To the number 41, append one digit to the left and one digit to the right so that the resulting four-digit number is divisible by 36. Find all solutions.
$\triangle$ Let's denote the unknown digits by $x$ and $y$. We apply the divisibility rule for 4 to the number $\overline{x 41 y}$:

$$
\overline{1 y}: 4
$$

Then $y=2$ or $y=6$. Let's consider both cases.

1) Suppose $y=2$.

We get the number $\overline{x 412}$. Based on the divisibility rule for 9,

$$
(x+4+1+2): 9, \quad(x+7): 9
$$

From this, $x=2$.

2) Suppose $y=6$.

Then

$$
\overline{x 416}: 9, \quad(x+4+1+6): 9, \quad(x+11): 9
$$

Therefore, $x=7$.

Answer: The four-digit number is 2412 or 7416.