olymmath

ISL 2019 N8

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

    Official text Transcription from NuminaMath olympiads, checked word for word against the official paper. Quoted with source.

    Official text: IMO 2019 Shortlist booklet, page 11.

    Solutions

    Official solution Solution 1 by the IMO Problem Selection Committee

    The terms of the source let olymmath link to this solution but not copy it. Read the solution (IMO official site).

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