1997 USAMO Problems/Problem 6

Revision as of 16:49, 13 June 2012 by Iwantcombo (talk | contribs) (Problem)

Problem

Suppose the sequence of nonnegative integers $a_1,a_2,...,a_{1997}$ satisfies

$a_i+a_j \le a_{i+j} \le a_i+a_j+1$

for all $i, j \ge 1$ with $i+j \le 1997$. Show that there exists a real number $x$ such that $a_n=\lfloor{nx}\rfloor$ (the greatest integer $\lenx$ (Error compiling LaTeX. ! Undefined control sequence.)) for all $1 \le n \le 1997$.

Solution

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

See Also

1997 USAMO (ProblemsResources)
Preceded by
Problem 5
Followed by
Last Problem
1 2 3 4 5 6
All USAMO Problems and Solutions
Invalid username
Login to AoPS