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Omni-MATH / The 2010 positive numbers a₁,a₂,…,a₂₀₁₀ satisfy

Problem

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problem

The 20102010 positive numbers a1,a2,…,a2010a_1, a_2, \ldots , a_{2010} satisfy the inequality aiaj≤i+ja_ia_j \le i+j for all distinct indices i,ji, j . Determine, with proof, the largest possible value of the product a1a2⋯a2010a_1a_2\cdots a_{2010} .
Plain-text mathematical notation (without MathML)
The 2010 positive numbers a₁,a₂,…,a₂₀₁₀ 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 a₁a₂⋯a₂₀₁₀ .
Original LaTeX notation
The $2010$ positive numbers $a_1, a_2, \ldots , a_{2010}$ satisfy
the inequality $a_ia_j \le i+j$ for all distinct indices $i, j$ .
Determine, with proof, the largest possible value of the product $a_1a_2\cdots a_{2010}$ .

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Source and history

task_id
f0e20bf3-5601-582a-9980-fe963f4c5356
task_key
test--f0e20bf3-5601-582a-9980-fe963f4c5356
task_revision_id
1
config / split
/ test

Official source

initial import