# Ceiling Function

#### anemone

##### MHB POTW Director
Staff member
Let $a$ and $b$ be two positive integers. Prove that the integer $a^2+\Bigl\lceil \dfrac{4a^2}{b}\Bigr\rceil$ is not a square.

(Here $\lceil z \rceil$ denotes the least integer greater than or equal to $z$.)