SEAMO 2027 - Paper E - SET 05 - Self-study Question 23

Let $a,b,c,d$ be four distinct positive real numbers satisfying $(a^{2012}-c^{2012})(a^{2012}-d^{2012})=2011$ and $(b^{2012}-c^{2012})(b^{2012}-d^{2012})=2011$. Find $(cd)^{2012}-(ab)^{2012}$.

Enter the number only.