Question 144
For any integer $k \in \mathbb{Z}$, we define the polynomial $F_k = X^4 + 2(1 - k)X^2 + (1 + k)^2$. Find all integers $k \in \mathbb{Z}$, such that $F_k$ is irreducible over $\mathbb{Z}$ but is reducible over $\mathbb{Z}_p$, for any prime $p$.