# Big degrees

Algebra Level pending

Let $$p(x)$$ be a nonzero polynomial of degree less than $$2014$$ that has no nonconstant factor in common with $$x^3-x$$. Let $\frac{d^{2014}}{dx^{2014}}\left(\frac{p(x)}{x^3-x}\right)=\frac{s(x)}{k(x)},$ where $$\frac{s(x)}{k(x)}$$ is in lowest terms. Find the smallest possible degree of $$s(x)$$.

(Based on 1992 Putnam Problem B4.)

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