Solutions of 2016

Algebra Level 5

If \(f(x)\) is a polynomial with integer coefficients, and \(a_{1}, a_{2}, a_{3}, a_{4}, a_{5}\) are distinct integers such that \(f(a_{1}) = f(a_{2}) = f(a_{3}) = f(a_{4}) = f(a_{5}) = 2015\), then find the number of integral solutions of the equation \(f(x) = 2016\).

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