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

Revision as of 08:14, 13 September 2012

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. Unknown error_msg)) for all $1 \le n \le 1997$ .

Solution

This problem needs a solution. If you have a solution for it, please help us out by adding it.

@@ Line 10: / Line 10: @@
 == See Also ==
-{{USAMO newbox|year=1997|num-b=5|after=Last Problem}}
+{{USAMO newbox|year=1997|num-b=5|after=Last Question}}
 [[Category:Olympiad Algebra Problems]]

1997 USAMO (Problems • Resources)
Preceded by Problem 5	Followed by Last Question
1 • 2 • 3 • 4 • 5 • 6
All USAMO Problems and Solutions

Page

Toolbox

Search

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

Revision as of 08:14, 13 September 2012

Problem

Solution

See Also