# A polynomial with integer values

Consider all polynomials $$f(x)$$ of degree 6 such that $$f(n)$$ is an integer for all integers $$n$$. The smallest possible positive leading coefficient of $$f(n)$$ can be expressed as $$\frac{a}{b}$$, where $$a$$ and $$b$$ are positive coprime integers. What is the value of $$a+b$$?

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