Difference between revisions of "2024 IMO Problems/Problem 1"
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is a multiple of <math>n</math>. (Note that <math>\lfloor z \rfloor</math> denotes the greatest integer less than or equal to <math>z</math>. For example, <math>\lfloor -\pi \rfloor = -4</math> and <math>\lfloor 2 \rfloor = \lfloor 2.9 \rfloor = 2</math>.) | is a multiple of <math>n</math>. (Note that <math>\lfloor z \rfloor</math> denotes the greatest integer less than or equal to <math>z</math>. For example, <math>\lfloor -\pi \rfloor = -4</math> and <math>\lfloor 2 \rfloor = \lfloor 2.9 \rfloor = 2</math>.) | ||
+ | |||
+ | ==Video Solution(In Chinese)== | ||
+ | https://youtu.be/LW54i7rWkpI | ||
+ | |||
+ | ==Video Solution== | ||
+ | https://www.youtube.com/watch?v=50W_ntnPX0k | ||
+ | |||
+ | ==Video Solution== | ||
+ | Part 1 (analysis of why there is no irrational solution) | ||
+ | |||
+ | https://youtu.be/QPdHrNUDC2A | ||
+ | |||
+ | Part 2 (analysis of even integer solutions and why there is no non-integer rational solution) | ||
+ | |||
+ | https://youtu.be/4rNh4sbsSms | ||
+ | |||
+ | ~Steven Chen (Professor Chen Education Palace, www.professorchenedu.com) | ||
+ | |||
+ | ==See Also== | ||
+ | |||
+ | {{IMO box|year=2024|before=First Problem|num-a=2}} |
Revision as of 13:23, 30 July 2024
Determine all real numbers such that, for every positive integer , the integer
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
2024 IMO (Problems) • Resources | ||
Preceded by First Problem |
1 • 2 • 3 • 4 • 5 • 6 | Followed by Problem 2 |
All IMO Problems and Solutions |