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

for all $i, j\ge1$ with $i+j\le1997$. 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\len\le1997\$ (Error compiling LaTeX. ! Undefined control sequence.).