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Omni-MATH / Given positive integers a₁,a₂,…,a₂₀₂₃ such that a_(k)=∑_(i=1)²⁰²³|a_(k)−a_(i)| for all 1≤k≤2023, find the minimum possible value of a₁+a₂+⋯+a₂₀₂₃.

Problem

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problem

Given positive integers a1,a2,…,a2023a_{1}, a_{2}, \ldots, a_{2023} such that ak=∑i=12023|ak−ai|a_{k}=\sum_{i=1}^{2023}\left|a_{k}-a_{i}\right| for all 1≤k≤20231 \leq k \leq 2023, find the minimum possible value of a1+a2+⋯+a2023a_{1}+a_{2}+\cdots+a_{2023}.
Plain-text mathematical notation (without MathML)
Given positive integers a₁,a₂,…,a₂₀₂₃ such that a_(k)=∑_(i=1)²⁰²³|a_(k)−a_(i)| for all 1≤k≤2023, find the minimum possible value of a₁+a₂+⋯+a₂₀₂₃.
Original LaTeX notation
Given positive integers \(a_{1}, a_{2}, \ldots, a_{2023}\) such that \(a_{k}=\sum_{i=1}^{2023}\left|a_{k}-a_{i}\right|\) for all \(1 \leq k \leq 2023\), find the minimum possible value of \(a_{1}+a_{2}+\cdots+a_{2023}\).

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Source and history

task_id
ce2e69f3-7a01-50b7-b035-85d199354590
task_key
test--ce2e69f3-7a01-50b7-b035-85d199354590
task_revision_id
1
config / split
/ test

Official source

initial import