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Suppose $f$ is a polynomial with integer coefficients, such that for all non-negative integers $n$ the $n$-th Fibonacci number $u_n$ divides $f(u_{n+1})$. Find the smallest possible positive value of $f(4)$.

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    This is a current problem at brilliant.org: http://brilliant.org/i/C4F9a6/. Moderators, please note.2012-12-29

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This is apparently a current problem at brilliant.org (h/t John Haussmann). I'm taking out my answer for now.