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

m
(added solution tag, USAMO box, and category.)
Line 7: Line 7:
  
 
== Solution ==
 
== Solution ==
 +
{{solution}}
 +
 +
== See Also ==
 +
{{USAMO newbox|year=1997|num-b=5|after=Last Problem}}
 +
 +
[[Category:Olympiad Algebra Problems]]

Revision as of 17:12, 12 April 2012

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.).

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