# A polynomial

Algebra Level 5

Let $$p(x)$$ be a polynomial of $$2015^\text{th}$$ degree. We know that for every integer $$k$$ with $$2 \le k \le 2017$$: $\large p(k) = \frac{k}{k^2-1}.$

Find the value of $$p(2018)$$. If this value can be expressed as $$\dfrac ab$$, where $$a$$ and $$b$$ are coprime positive integers, submit your answer as $$b$$.

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