IMO Shortlist 1987 problem 3
Dodao/la:
arhiva2. travnja 2012. Does there exist a second-degree polynomial
![p(x, y)](/media/m/1/6/0/160d7873ebf0385b8b45292ffe729bcc.png)
in two variables such that every non-negative integer
![n](/media/m/a/e/5/ae594d7d1e46f4b979494cf8a815232b.png)
equals
![p(k,m)](/media/m/9/3/9/93948ea05302931da731a984b7cef4c9.png)
for one and only one ordered pair
![(k,m)](/media/m/c/b/5/cb5ef9862bda3c8fb86f1deb1da10cb1.png)
of non-negative integers?
Proposed by Finland.
%V0
Does there exist a second-degree polynomial $p(x, y)$ in two variables such that every non-negative integer $n$ equals $p(k,m)$ for one and only one ordered pair $(k,m)$ of non-negative integers?
Proposed by Finland.
Izvor: Međunarodna matematička olimpijada, shortlist 1987