A question for fun

by Admin MathWit - Suppose that \(a,b\) are positive integers and \(a^{2012} + b^{2012} = 2^{2013}\), then what can you say about \(\left(\frac{a-b}{a+b}\right)^{2014}?\)

The question itself is a big hint, so this problem is not as hard as it looks! Enjoy!