The fifth operator

2012 is divisible by 4 so remainder is 0

${ 2012 }^{ 2012 }\quad \left( {\text{mod}}\quad 4 \right) =x$

Apart from the obvious fact that 2012 is divisible by 4, we can also use programming to directly compute the answer due to the current computation speed Here's the code:

1
2

>>> (2012 ** 2012) % 4
0