showthatFibonaccinumberssatisfytherecurrencerelationfn=5f(n-4)+3f(n-5)forn=5,6,7...,togetherwiththeinitialconditionsf0=0,f1=1,f2=1,f3=2,f4=3.usethisrecurrencerelationtoshowthatf5nisdivisibleby5,forn=1,2,3...
注:fibonaccinumber满足fn=f(n-1)+f(n-2)