Difference between revisions of "2010 IMO Problems/Problem 6"
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| + | == Solution == | ||
| + | {{solution}} | ||
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| + | == See Also == | ||
| + | {{IMO box|year=2010|num-b=5|After=Last Question}} | ||
| + | [[Category:Olympiad Number Theory Problems]] | ||
Revision as of 17:50, 3 April 2012
Problem
Let 
be a sequence of positive real numbers, and 
be a positive integer, such that
![\[a_n = \max \{ a_k + a_{n-k} \mid 1 \leq k \leq n-1 \} \ \textrm{ for all } \ n > s.\]](http://latex.artofproblemsolving.com/f/1/2/f12c9c5e0f154549118a33a2f359329333f432a7.png)
Prove there exist positive integers 
and 
, such that
![\[a_n = a_{\ell} + a_{n - \ell} \ \textrm{ for all } \ n \geq N.\]](http://latex.artofproblemsolving.com/b/0/b/b0b2bd4507621302eeee27ae50ed9c0afd72c6ef.png)
Author: Morteza Saghafiyan, Iran
Solution
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See Also
| 2010 IMO (Problems) • Resources | ||
| Preceded by Problem 5 |
1 • 2 • 3 • 4 • 5 • 6 | Followed by [[2010 IMO Problems/Problem {{{num-a}}}|Problem {{{num-a}}}]] |
| All IMO Problems and Solutions | ||
