Question 4
(CAN) Let $\{f_n\}$ be the Fibonacci sequence $\{1,1,2,3,5,\ldots\}$.
(a) Find all pairs $(a,b)$ of real numbers such that for each $n$, $af_n+bf_{n+1}$ is a member of the sequence.
(b) Find all pairs $(u,v)$ of positive real numbers such that for each $n$, $uf_n^2+vf_{n+1}^2$ is a member of the sequence.
(a) Find all pairs $(a,b)$ of real numbers such that for each $n$, $af_n+bf_{n+1}$ is a member of the sequence.
(b) Find all pairs $(u,v)$ of positive real numbers such that for each $n$, $uf_n^2+vf_{n+1}^2$ is a member of the sequence.