2023 IMO Problems/Problem 4
Contents
[hide]Problem
Let be pairwise different positive real numbers such that is an integer for every . Prove that .
Video Solution(中文讲解)subtitle in English
Video Solution
https://www.youtube.com/watch?v=jZNIpapyGJQ [Video contains solutions to all day 2 problems]
Solution
We solve for in terms of and
Again, by AM-GM, the above equation becomes
Hence, but equality is achieved only when and are equal. They can never be equal because there are no two equal So
See Also
2023 IMO (Problems) • Resources | ||
Preceded by Problem 3 |
1 • 2 • 3 • 4 • 5 • 6 | Followed by Problem 5 |
All IMO Problems and Solutions |