# Does This Polynomial Even Exist?

Find the number of positive integers $$n$$ such that $$2 \leq n \leq 100$$ and there exists a polynomial $$f(x)$$ with real coefficients and degree $$<n$$ such that for all integers $$x,$$ $$f(x)$$ is an integer if and only if $$x$$ is not a multiple of $$n.$$

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