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USAMO
2010
Problem - 3441
The 2010 positive numbers
a
1
,
a
2
,
…
,
a
2010
satisfy the inequality
a
i
a
j
≤
i
+
j
for all distinct indices
i
,
j
. Determine, with proof, the largest possible value of the product
a
1
a
2
…
a
2010
.
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