### Finding the minimum mulitplier for a sequence of consecutive Fibonacci numbers

The Fibonacci numbers F_{1},F_{2},... are defined by F_{1}=1=F_{2} and F_{m}=F_{m-1}+F_{m-2} for m ≥ 3.

F_{m}=(α^{m}-β^{m})/√5, where α=(1+√5)/2 and β=(1-√5)/2.

We use formulae from *Minimal multipliers for consecutive Fibonacci numbers*, K.R. Matthews, Acta Arith. 75 (1996) 205-218 to compute the unique multiplier vector (x_{1}, , ,x_{m}) of minimum Euclidean norm for m consecutive Fibonacci numbers F_{n},...,F_{n+m-1}.
See formula for x_{i}.

*Last modified 30th April 2013*

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