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Russian NT with a Ceiling

Source: 2019 ISL N8

September 22, 2020
ceiling functionnumber theoryIMO ShortlistIMO Shortlist 2019Perfect Square

Problem Statement

Let aa and bb be two positive integers. Prove that the integer a2+⌈4a2b⌉a^2+\left\lceil\frac{4a^2}b\right\rceil is not a square. (Here ⌈z⌉\lceil z\rceil denotes the least integer greater than or equal to zz.)
Russia
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