What is the last digit of $2003^{2003}$? 
What is the last digit of this number?
$$2003^{2003}$$

Thanks in advance.
I don't have any kind of idea how to solve this. Except that $3^3$ is $27$.

Since we have
$$3^1=\color{red}{3},3^2=\color{red}{9},3^3=2\color{red}{7},3^4=8\color{red}{1},3^5=24\color{red}{3},\cdots.$$
and $$2003\equiv 3\pmod 4,$$
the right-most digit of $2003^{2003}$ is the same as the right-most digit of $3^3=27$.
