Question 92
Let $a_1 = 1$, $a_2 = 10$ and $a_{n+1} = 2a_n + 3a_{n-1}$, $n \gt 1$. Then the infinite sum
$$
P(x) = \sum_{i=1}^{\infty} a_i x^i,
$$
is defined and finite for $x \in ] -\frac{1}{3}, \frac{1}{3}[$. Find all $y \in \mathbb{Z}$ such that
$$
P\left(\frac{1}{y}\right) \in \mathbb{Z}.
$$
$$
P(x) = \sum_{i=1}^{\infty} a_i x^i,
$$
is defined and finite for $x \in ] -\frac{1}{3}, \frac{1}{3}[$. Find all $y \in \mathbb{Z}$ such that
$$
P\left(\frac{1}{y}\right) \in \mathbb{Z}.
$$