How do I find the last two digits $2012^{2013}$? How do I find the last two digits 20122013
My teacher said this was simple arithmetics(I still don't see how this is simple).
I thought of using Congruence equation as 2012 is congruent to 2 mod 10...but i can't get 22013
Can anyone help please?

Working in mod $100$, we have $$12^{21} \equiv 12$$ 
Thus $$2012^{2013}\equiv 12^{2013} \equiv 12^{21\times 95+18} \equiv 12^{95} \times 12^{18} \equiv 12^{113} \equiv 12^{21\times 5+8}\equiv 12^{13}\equiv 72$$
