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2024 IMO Problems/Problem 1

Revision as of 11:33, 16 July 2024 by I andrea (talk | contribs)

Find all real numbers $\alpha$ such that for any positive integer $n$ the integer

\[\lfloor \alpha \rfloor + \lfloor 2\alpha \rfloor + \dots +\lfloor n\alpha \rfloor\]

is divisible by $n$.

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