Difference between revisions of "2024 IMO Problems/Problem 1"
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| + | Find all real numbers <math>\alpha</math> such that for any positive integer <math>n</math> the integer | ||
| + | <cmath>\lfloor \alpha \rfloor + \lfloor 2\alpha \rfloor + \dots +\lfloor n\alpha \rfloor</cmath> | ||
| + | |||
| + | is divisible by <math>n</math>. | ||
Revision as of 11:33, 16 July 2024
Find all real numbers 
such that for any 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 divisible by .
