1997 USAMO Problems/Problem 6

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

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1997 USAMO (Problems • Resources)
Preceded by Problem 5	Followed by Last Problem
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1997 USAMO Problems/Problem 6

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