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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 Moderators, please note. – Jon Haussmann Dec 29 '12 at 0:49
The above question is posted as a Challenge problem on, which offers weekly problem sets to test student's problem solving abilities. John Chang has been posting questions on and expecting others to solve the problems for him. He has posted another one of our questions at… -Calvin Lin Mathematics Challenge Master – Calvin Lin Dec 29 '12 at 1:05

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

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