Finding the minimum mulitplier for a sequence of consecutive Fibonacci numbers

The Fibonacci numbers F1,F2,... are defined by F1=1=F2 and Fm=Fm-1+Fm-2 for m ≥ 3.
Fm=(αm-βm)/√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 (x1, , ,xm) of minimum Euclidean norm for m consecutive Fibonacci numbers Fn,...,Fn+m-1.

See formula for xi.

Enter n (1 ≤ n ≤ 100):
Enter m (2 ≤ m ≤ 50):

Last modified 30th April 2013
Return to main page