211. Is the difference $17^{15}-3^{15}$ divisible by 4?
$\triangle$ The difference of the bases of the powers $17-3=14$ is divisible by 2, but not by 4. This does not mean that the given difference $17^{15}-3^{15}$ is not divisible by 4. Let's factorize it using the formula (1:

$$
17^{15}-3^{15}=14 \cdot\left(17^{14}+17^{13} \cdot 3+17^{12} \cdot 3^{2}+\ldots+3^{14}\right)
$$

Inside the parentheses, there are only odd terms. How many are there? Recall that when factoring the difference $a^{n}-b^{n}$, the number of terms in the second factor is equal to $n$. Here $n=15$, so the number of terms in the written sum is 15. Therefore, this sum is odd.

Answer: does not divide.