TW-TST 1995 Problem 4

Let $m_{1},m_{2},...,m_{n}$ be mutually distinct integers. Prove that there exists a $f(x)\in\mathbb{Z}[x]$ of degree $n$ satisfying the following two conditions: a) $f(m_{i})=-1\forall i=1,2,...,n$ . b) $f(x)$ is irreducible.