# An algebra problem by Vishnu Kadiri

Algebra Level 3

Let $$P_1 = x^2 + a_1 x + b_1$$ and $$P_2 = x^2 + a_2 x + b_2$$ be polynomials with integer coefficients, and $$a_1 \ne a_2$$. Suppose there exists some integers $$m$$ and $$n$$ satisfying $$P_1(m) = P_2 (n)$$ and $$P_1 (n) = P_2 (m)$$, what can we conclude about the value of $$a_1 - a_2$$?

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