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[\sqrt{n} ] -1 divides n + 1, [\sqrt{n} ]+2 divides n + 4

Source: 2022 Mathematics Regional Olympiad of Mexico West P5

October 6, 2022
floor functionnumber theorydivides

Problem Statement

Determine all positive integers nn such that ⌊n⌋−1\lfloor \sqrt{n} \rfloor - 1 divides n+1n + 1 and ⌊n⌋+2\lfloor \sqrt{n} \rfloor +2 divides n+4 n + 4.
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