MathDB
L 4

Source:

May 25, 2007
inductionLinear Recurrences

Problem Statement

The Fibonacci sequence {Fn}\{F_{n}\} is defined by F1=1,  F2=1,  Fn+2=Fn+1+Fn.F_{1}=1, \; F_{2}=1, \; F_{n+2}=F_{n+1}+F_{n}. Show that Fmn−Fn+1m+Fn−1mF_{mn}-F_{n+1}^{m}+F_{n-1}^{m} is divisible by Fn3F_{n}^{3} for all m≥1m \ge 1 and n>1n>1.
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