Question 22
N4 (BUL) Find all positive integers $a$ and $b$ for which
$$\left[\frac{a^2}b\right]+\left[\frac{b^2}a\right]=\left[\frac{a^2+b^2}{ab}\right]+ab$$
where as usual, $[t]$ refers to greatest integer that is less than or equal to $t$.
$$\left[\frac{a^2}b\right]+\left[\frac{b^2}a\right]=\left[\frac{a^2+b^2}{ab}\right]+ab$$
where as usual, $[t]$ refers to greatest integer that is less than or equal to $t$.