Call a polynomial f(x) excellent if its coefficients are all in [0, 1) and f(x) is an integer for all integers x. (a) Compute the number of excellent polynomials with degree at most 3. (b) Compute the number of excellent polynomials with degree at most n, in terms of n. (c) Find the minimum n ≥ 3 for which there exists an excellent polynomial of the form +g(x), where g(x) is a polynomial of degree at most n - 3.

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