# Difference between revisions of "1997 USAMO Problems/Problem 6"

## 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

 1997 USAMO (Problems • Resources) Preceded byProblem 5 Followed byLast Problem 1 • 2 • 3 • 4 • 5 • 6 All USAMO Problems and Solutions