Difference between revisions of "2024 IMO Problems/Problem 1"
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~Steven Chen (Professor Chen Education Palace, www.professorchenedu.com) | ~Steven Chen (Professor Chen Education Palace, www.professorchenedu.com) | ||
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| + | {{IMO box|year=2023|before=First Problem|num-a=2}} | ||
Revision as of 12:23, 30 July 2024
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 
.)
Video Solution(In Chinese)
Video Solution
https://www.youtube.com/watch?v=50W_ntnPX0k
Video Solution
Part 1 (analysis of why there is no irrational solution)
Part 2 (analysis of even integer solutions and why there is no non-integer rational solution)
~Steven Chen (Professor Chen Education Palace, www.professorchenedu.com)
See Also
| 2023 IMO (Problems) • Resources | ||
| Preceded by First Problem |
1 • 2 • 3 • 4 • 5 • 6 | Followed by Problem 2 |
| All IMO Problems and Solutions | ||
