ABC do 2

Algebra Level 3

Given that \(P_1(x) = x^2 + a_1 x + b_1 \) and \(P_2(x) = x^2 + a_2 x + b_2\) are two quadratic polynomials with integer coefficients such that \(P_1(m) = P_2 (n) \), \(P_1(n)= P_2(m) \), \(a_1 \ne a_2 \), and \(m\) and \(n\) are distinct integers. What can be said about \(a_1 \)+\(a_2 \)?

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