MathDB

4

Part of 1981 IMO Shortlist

Problems(1)

On Fibonacci Sequence

Source:

9/15/2010
Let {fn}\{fn\} be the Fibonacci sequence {1,1,2,3,5,… .}.\{1, 1, 2, 3, 5, \dots.\}.
(a) Find all pairs (a,b)(a, b) of real numbers such that for each nn, afn+bfn+1af_n +bf_{n+1} is a member of the sequence.
(b) Find all pairs (u,v)(u, v) of positive real numbers such that for each nn, ufn2+vfn+12uf_n^2 +vf_{n+1}^2 is a member of the sequence.
algebraFibonacciFibonacci sequenceSequenceIMO Shortlistnumber theory