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

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== Problem ==
 
Suppose the sequence of nonnegative integers <math>a_1,a_2,...,a_{1997}</math> satisfies
 
  
<math>a_i+a_j\lea_{i+j}\lea_i+a_j+1</math>
 
 
for all <math>i, j\ge1</math> with <math>i+j\le1997</math>. Show that there exists a real number <math>x</math> such that <math>a_n=\lfloor{nx}\rfloor</math> (the greatest integer <math>\lenx</math>) for all <math>1\len\le1997</math>.
 
 
== Solution ==
 

Revision as of 20:10, 1 July 2011

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