Question 32
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.)