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Find all positive integers $a$ and $b$ for which $$\left\lfloor\frac{a^{2}}{b}\right\rfloor+\left\lfloor\frac{b^{2}}{a}\right\rfloor =\left\lfloor\frac{a^{2}+b^{2}}{ab}\right\rfloor+ab.$$
Source: Međunarodna matematička olimpijada, shortlist 1996
Školjka 
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