2010 IMO Problems/Problem 6

Problem

Let $a_1, a_2, a_3, \ldots$ be a sequence of positive real numbers, and $s$ be a positive integer, such that \[a_n = \max \{ a_k + a_{n-k} \mid 1 \leq k \leq n-1 \} \ \textrm{ for all } \ n > s.\] Prove there exist positive integers $\ell \leq s$ and $N$, such that \[a_n = a_{\ell} + a_{n - \ell} \ \textrm{ for all } \ n \geq N.\]

Author: Morteza Saghafiyan, Iran

Solution

This problem needs a solution. If you have a solution for it, please help us out by adding it.

See Also

2010 IMO (Problems) • Resources)
Preceded by
Problem 5
1 2 3 4 5 6 Followed by
Last Question
All IMO Problems and Solutions
Invalid username
Login to AoPS