# Is it a Diophantine?

Number Theory Level 5

$\large \left \lfloor \frac{a^2}b \right \rfloor + \left\lfloor \frac{b^2}a \right \rfloor = \left \lfloor \frac{a^2+b^2}{ab} \right \rfloor + ab$

Given $$a$$ and $$b$$ are positive integers with $$a<100$$, if the ordered pairs $$(a_1, b_1)$$, $$(a_2, b_2)$$, $$\ldots$$ , $$(a_k, b_k)$$ satisfy the equation above, evaluate $$\displaystyle \sum_{i=1}^{k} (a_i+b_i)$$.

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