IMO Shortlist 2010 problem N5
Dodao/la:
arhiva23. lipnja 2013. Find all functions
![g:\mathbb{N}\rightarrow\mathbb{N}](/media/m/7/f/5/7f59d775825ccef27b36a157e3d8f41d.png)
such that
![\left(g(m)+n\right)\left(g(n)+m\right)](/media/m/6/f/3/6f3b43315b865b531bc2e1d5e060ee2d.png)
is perfect square for all
![m,n\in\mathbb{N}.](/media/m/e/5/3/e53942e536953457695aada3961b80c4.png)
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
Izvor: Međunarodna matematička olimpijada, shortlist 2010