IMO Shortlist 1996 problem N4


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2. travnja 2012.
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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.
Izvor: Međunarodna matematička olimpijada, shortlist 1996