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

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

Revision as of 09:14, 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. ! Undefined control sequence.)) for all $1 \le n \le 1997$.

Solution

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See Also

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