# Divisive succession

Number Theory Level pending

Find the largest integer $$n$$, such that for some non-constant cubic polynomial $$f(x)$$ with integer coefficients,

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

Details and assumptions

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

The divisibility condition is a statement about integers, not polynomial.

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