Solutions of 2016

Algebra Level 4

If f(x)f(x) is a polynomial with integer coefficients, and a1,a2,a3,a4,a5a_{1}, a_{2}, a_{3}, a_{4}, a_{5} are distinct integers such that f(a1)=f(a2)=f(a3)=f(a4)=f(a5)=2015f(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)=2016f(x) = 2016.

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