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Ceiling Function

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MHB POTW Director
Staff member
Feb 14, 2012
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 $z$.)