(a) Find all pairs of real numbers such that for each , is a member of the sequence.
(b) Find all pairs of positive real numbers such that for each , is a member of the sequence.
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Let $\{fn\}$ be the Fibonacci sequence $\{1, 1, 2, 3, 5, \dots.\}.$
(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.
Izvor: Međunarodna matematička olimpijada, shortlist 1981
Školjka 
be the Fibonacci sequence 
of real numbers such that for each 
, 
is a member of the sequence.
of positive real numbers such that for each 
is a member of the sequence.