IMO Shortlist 2009 problem A5
Dodao/la:
arhiva2. travnja 2012. Let
![f](/media/m/9/9/8/99891073047c7d6941fc8c6a39a75cf2.png)
be any function that maps the set of real numbers into the set of real numbers. Prove that there exist real numbers
![x](/media/m/f/1/8/f185adeed9bd346bc960bca0147d7aae.png)
and
![y](/media/m/c/c/0/cc082a07a517ebbe9b72fd580832a939.png)
such that
![f\left(x-f(y)\right)>yf(x)+x](/media/m/6/5/a/65a97d856311e34a1edce2eba6187679.png)
Proposed by Igor Voronovich, Belarus
%V0
Let $f$ be any function that maps the set of real numbers into the set of real numbers. Prove that there exist real numbers $x$ and $y$ such that $$f\left(x-f(y)\right)>yf(x)+x$$
Proposed by Igor Voronovich, Belarus
Izvor: Međunarodna matematička olimpijada, shortlist 2009