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

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== 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


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.).


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See Also

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