2024 IMO Problems/Problem 3
Let be an infinite sequence of positive integers, and let be a positive integer. Suppose that, for each , is equal to the number of times appears in the list .
Prove that at least one of the sequence and is eventually periodic.
(An infinite sequence is eventually periodic if there exist positive integers and such that for all .)
Video Solution
https://youtu.be/ASV1dZCuWGs (in full detail!)
See Also
2024 IMO (Problems) • Resources | ||
Preceded by Problem 2 |
1 • 2 • 3 • 4 • 5 • 6 | Followed by Problem 4 |
All IMO Problems and Solutions |