Solve the inequality in integers: $x^{2}<3-2 \cos \pi x$.

#
$x^{2}<3-2 \cos \pi x<5$. Therefore, integer solutions of the inequality can only be among the numbers $0, \pm 1, \pm 2$. Considering that both sides of the inequality are even functions, it is sufficient to check the numbers 0, 1, and 2. In doing so, we verify that the numbers 0 and 1 are solutions, while the number 2 is not.

## Answer

$0, \pm 1$.