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 13:09, 5 July 2011
Problem
Suppose the sequence of nonnegative integers 
satisfies
$a_i+a_j\lea_{i+j}\lea_i+a_j+1$ (Error compiling LaTeX. Unknown error_msg)
for all 
with 
. Show that there exists a real number 
such that 
(the greatest integer $\lenx$ (Error compiling LaTeX. Unknown error_msg)) for all $1\len\le1997$ (Error compiling LaTeX. Unknown error_msg).
