Find the largest possible integer $$n$$ such that there exists a non-constant quadratic polynomial $$f(x)$$ with integer coefficients satisfying

$f(1) \mid f(2), f(2) \mid f(3), \ldots f(n−1) \mid f(n).$

Details and assumptions

For (possibly negative or zero) integers $$m$$ and $$k$$ the notation $$m \mid k$$ means that $$k=m\cdot i$$ for some integer $$i.$$

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