A Strange Polynomial in 2015

Algebra Level 5

Let \(f(x)\) be a polynomial with integer coefficients such that

\[ f(2) = f(0) = f(1) = f(5) = n \\ f(-2) = f(-1) = f(-5) = -n \]

for some positive integer \(n\). Find the smallest possible value of \(n\).

Inspired from an AMC 10B problem.
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