Question 96
Let $a$ and $b$ be two positive integers. Prove that the integer
$$
a^{2} + \left\lceil \frac{4 a^{2}}{b} \right\rceil
$$
is not a square. (Here $\lceil z\rceil$ denotes the least integer greater than or equal to $z$.)
$$
a^{2} + \left\lceil \frac{4 a^{2}}{b} \right\rceil
$$
is not a square. (Here $\lceil z\rceil$ denotes the least integer greater than or equal to $z$.)