IMO Shortlist 2010 problem N5
Find all functions
such that
is perfect square for all
Proposed by Gabriel Carroll, USA
%V0
Find all functions $g:\mathbb{N}\rightarrow\mathbb{N}$ such that
$$\left(g(m)+n\right)\left(g(n)+m\right)$$
is perfect square for all $m,n\in\mathbb{N}.$
Proposed by Gabriel Carroll, USA
Source: Međunarodna matematička olimpijada, shortlist 2010
Školjka 
