# 1997 USAMO Problems/Problem 6

## Problem

Suppose the sequence of nonnegative integers satisfies

$a_i+a_j\lea_{i+j}\lea_i+a_j+1$ (Error compiling LaTeX. ! Undefined control sequence.)

for all with . Show that there exists a real number such that (the greatest integer $\lenx$ (Error compiling LaTeX. ! Undefined control sequence.)) for all $1\len\le1997$ (Error compiling LaTeX. ! Undefined control sequence.).