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