# Fibonacci-Factors Polynomial

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

Details and assumptions

The Fibonacci numbers are defined as follows:

$$u_1=1,\ u_2=1;$$ $$u_n=u_{n-1}+u_{n-2}$$ for all $$n\geq 3$$.

0 is not a positive number.

×