+0  
 
-1
80
1
avatar

The Lucas numbers L_n are given by the recursion L_0=2, L_1=1 and L_n=L_n-1+L_n-2. Find the units digit of L_{100}.

 Apr 29, 2022
 #1
avatar+124598 
+1

Formula  for the nth Lucas number  =

 

Lucas(n) = Phi^n + ( –phi )^n

 

Where   Phi   =     (1 + sqrt 5)/ 2

And phi  =  ( sqrt 5 - 1 ) / 2

 

So

 

L (100)  =    [ (1 + sqrt 5)/2 ]^100 +  [ (-1)( sqrt 5 - 1)/2 ]^100  = 792070839848372253127

 

 

cool cool cool

 Apr 29, 2022

25 Online Users

avatar