Difference between revisions of "2024 IMO Problems/Problem 1"
Bobwang001 (talk | contribs) (→Video Solution) |
Bobwang001 (talk | contribs) (→Video Solution(In Chinese)) |
||
| Line 6: | Line 6: | ||
==Video Solution(In Chinese)== | ==Video Solution(In Chinese)== | ||
| − | https:// | + | https://youtu.be/LW54i7rWkpI |
==Video Solution== | ==Video Solution== | ||
Revision as of 23:11, 26 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)
