Solutions of 2016

Algebra Level 4

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 $f(x) = 2016$ .

Solutions of 2016

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