MathDB

equation

Source: Baltic Way 2009

November 12, 2009

functionalgebra proposedalgebra

Problem Statement

Let

f_0=f_1=1

and

f_{i+2}=f_{i+1}+f_i

for all

n\ge 0

. Find all real solutions to the equation

x^{2010}=f_{2009}\cdot x+f_{2008}