MathDB

N8

Part of 2019 IMO Shortlist

Problems(1)

Russian NT with a Ceiling

Source: 2019 ISL N8

9/22/2020
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
ceiling functionnumber theoryIMO ShortlistIMO Shortlist 2019Perfect Square