A Fibonacci Number System

Ken Levasseur Mathematical Sciences UMass Lowell Kenneth_Levasseur@uml.edu

The Fibonacci sequence is defined recursively by f_n= f_n-1 + f_n-2, with f₁ = f₂ = 1.

A problem posed by Elias Lapakis in the December 2002 issue of Mathematics Magazine is to prove that every positive integer n can be expressed in the form

where k is a posive integer and integers a₁, a₂, ..., a_k all equal 1 or 2.

Maybe after the deadline for solving the problem, I'll outline the algorithm behind this page. The output is a list of coefficients {a₁,..., a_k}. This list isn't unique, but the output given has, I believe the minimum length among all solutions.

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