222. Given a sequence of polynomials:

\[
\begin{gathered}
P_{1}=1, P_{2}=x, P_{3}=x \cdot P_{2}-P_{1}, P_{4}=x \cdot P_{3}- \\
-P_{2}, \ldots, P_{n}=x \cdot P_{n-1}-P_{n-2 .}
\end{gathered}
\]

1) For which integer values of \( x \) is the number \( P_{5} \) divisible by 5?
2) Is \( P_{5} \) divisible by 10?
3) Show that \( P_{6} \) is divisible by 6 for any integer \( x \).
4) For which integer values of \( x \) is the number \( P_{7} \) divisible by 7?
222. 223) $P_{5}=x^{4}-3 x^{2}+1 ; x=5 t \pm 2$.
2) $P_{5}$ cannot be divisible by 10, since for any integer $x$ the number $x^{4}-3 x^{2}+1$ is odd.
3) $P_{6}=x(x-1)(x+1)\left(x^{2}-3\right)$ is divisible by 6, since the product of three consecutive numbers is divisible by $1 \cdot 2 \cdot 3=6$.
4) $x=7 t \pm 2$.