IMO Shortlist 1996 problem N4
Dodao/la:
arhiva2. travnja 2012. Find all positive integers
![a](/media/m/6/d/2/6d2832265560bb67cf117009608524f6.png)
and
![b](/media/m/e/e/c/eec0d7323095a1f2101fc1a74d069df6.png)
for which
%V0
Find all positive integers $a$ and $b$ for which $$\left\lfloor\frac{a^{2}}{b}\right\rfloor+\left\lfloor\frac{b^{2}}{a}\right\rfloor =\left\lfloor\frac{a^{2}+b^{2}}{ab}\right\rfloor+ab.$$
Izvor: Međunarodna matematička olimpijada, shortlist 1996