Quadratika

Let $P_1(x$ ) $=$ $x^2$ $+$ $a_1x$ $+$ $b_1$ and $P_2(x)$ $=$ $x^2$ $+$ $a_2x$ $+$ $b_2$ be two quadratic polynomials with integer coefficients. Suppose $a_1$ and $a_2$ are distinct and there exist distinct integers $m$ and $n$ such that $P_1(m)$ $=$ $P_2(n)$ and also $P_2(m)$ $=$ $P_1(n)$ . We can conclude that $a_1$ $-$ $a_2$ is always :