2019 IMO Shortlist N8

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 $z$.)

设$a$和$b$为两个正整数。证明整数 $$a^{2}+\left\lceil\frac{4 a^{2}}{b}\right\rceil$$ 不是正方形。 (这里$\lceil z\rceil$表示大于或等于$z$的最小整数。)