MathDB

4

Part of PEN L Problems

Problems(1)

L 4

Source:

5/25/2007
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.
inductionLinear Recurrences