This year is not 2013

Relevant wiki: Finding the Last Digit of a Power

by a theorem stated in the relevant wiki, $2013^ 2013=2013^ 13$ $mod 100$ . so just calculate that

edit: it's 2013^2013=2013^13 not the thing it says in the latex. Latex doesn't allow you to put multiple digits in the exponent. sorry about that

The main thing which we need to find out here is the last two digits of 13^2013 by Binomial theorem now,we know that 13 and 100 are two co-prime numbers.So we can apply the Euler's totient theorem.Applying this theorem we will get that 13^40=1(mod 100) that implies 13^2000=1(mod100).Now you can calculate.