Fibonacci-Factors Polynomial
Number Theory
Level
5
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.
by
Calvin Lin