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Triangular Numbers in action

Source: RMO 2018 P5

October 7, 2018
algebranumber theoryDivisibility

Problem Statement

Find all natural numbers nn such that 1+[2n] 1+[\sqrt{2n}]~ divides 2n2n.
( For any real number xx , [x][x] denotes the largest integer not exceeding xx. )
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