Turkish NMO First Round - 2012 Problem - 31 {Algebra}
Source:
July 1, 2012
Problem Statement
f:Z→Z satisfies m+f(m+f(n+f(m)))=n+f(m) for every integers m,n.
If f(6)=6, then f(2012)=?<spanclass=′latex−bold′>(A)</span>−2010<spanclass=′latex−bold′>(B)</span>−2000<spanclass=′latex−bold′>(C)</span>2000<spanclass=′latex−bold′>(D)</span>2010<spanclass=′latex−bold′>(E)</span>2012