2024 IMO Problems/Problem 1
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Determine all real numbers 
such that, for every positive integer 
, the integer
![\[\lfloor \alpha \rfloor + \lfloor 2\alpha \rfloor + \dots +\lfloor n\alpha \rfloor\]](http://latex.artofproblemsolving.com/d/e/8/de8ec4b01ecf552960e95a201881ef7e35e7a2ce.png)
is a multiple of . (Note that 
denotes the greatest integer less than or equal to 
. For example, 
and 
.)
