IMO Shortlist 1996 problem N5
Dodao/la:
arhiva2. travnja 2012. Show that there exists a bijective function
![f: \mathbb{N}_{0}\to \mathbb{N}_{0}](/media/m/7/9/4/79421dd24443a6ca3c68ddcb4e95ecb0.png)
such that for all
![m,n\in \mathbb{N}_{0}](/media/m/3/b/2/3b2bbf3926a694167d98c828c966eb57.png)
:
%V0
Show that there exists a bijective function $f: \mathbb{N}_{0}\to \mathbb{N}_{0}$ such that for all $m,n\in \mathbb{N}_{0}$:
$$f(3mn + m + n) = 4f(m)f(n) + f(m) + f(n).$$
Izvor: Međunarodna matematička olimpijada, shortlist 1996