Task B-3.3. Determine all integers $k$ for which the equation $x^{2014} + k x^{2} + 36 = 0$ has at least one integer solution.
## First solution.

Let $x_{0}$ be an integer solution of the equation $x^{2014} + k x^{2} + 36 = 0$.

Then $k = -x_{0}^{2012} - \frac{36}{x_{0}^{2}}$.

For $k$ to be an integer, $x_{0}^{2}$ must be a divisor of 36,

i.e., $x_{0}^{2} \in \{1, 4, 9, 36\}$.

It follows that $k \in \left\{-37, -4^{1006} - 9, -9^{1006} - 4, -36^{1006} - 1\right\}$.

(2 points)