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 \(a_1 - a_2\)?

×

Problem Loading...

Note Loading...

Set Loading...