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Omni-MATH / Let a₁,a₂,…,a_(n) be a sequence of distinct positive integers such that a₁+a₂+⋯+a_(n)=2021 and a₁a₂⋯a_(n) is maximized. If M=a₁a₂⋯a_(n), compute the largest positive integer k such…

Problem

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problem

Let a1,a2,…,ana_{1}, a_{2}, \ldots, a_{n} be a sequence of distinct positive integers such that a1+a2+⋯+an=2021a_{1}+a_{2}+\cdots+a_{n}=2021 and a1a2⋯ana_{1} a_{2} \cdots a_{n} is maximized. If M=a1a2⋯anM=a_{1} a_{2} \cdots a_{n}, compute the largest positive integer kk such that 2k∣M2^{k} \mid M.
Plain-text mathematical notation (without MathML)
Let a₁,a₂,…,a_(n) be a sequence of distinct positive integers such that a₁+a₂+⋯+a_(n)=2021 and a₁a₂⋯a_(n) is maximized. If M=a₁a₂⋯a_(n), compute the largest positive integer k such that 2^(k)∣M.
Original LaTeX notation
Let $a_{1}, a_{2}, \ldots, a_{n}$ be a sequence of distinct positive integers such that $a_{1}+a_{2}+\cdots+a_{n}=2021$ and $a_{1} a_{2} \cdots a_{n}$ is maximized. If $M=a_{1} a_{2} \cdots a_{n}$, compute the largest positive integer $k$ such that $2^{k} \mid M$.

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Source and history

task_id
77f93a0e-9e1f-523f-a916-2f9f6d1fa23e
task_key
test--77f93a0e-9e1f-523f-a916-2f9f6d1fa23e
task_revision_id
1
config / split
/ test

Official source

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