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}.
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
