Školjka

%V0 Find all positive integers $a$ and $b$ for which $$\left\lfloor\frac{a^{2}}{b}\right\rfloor+\left\lfloor\frac{b^{2}}{a}\right\rfloor =\left\lfloor\frac{a^{2}+b^{2}}{ab}\right\rfloor+ab.$$