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Omni-MATH / For a given integer n≥2, let a₀,a₁,…,a_(n) be integers satisfying 0=a₀<a₁<…<a_(n)=2n−1. Find the smallest possible number of elements in the set {a_(i)+a_(j)∣0≤i≤j≤n}.

Problem

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problem

For a given integer n≥2n\ge 2, let a0,a1,…,ana_0,a_1,\ldots ,a_n be integers satisfying 0=a0<a1<…<an=2n−10=a_0<a_1<\ldots <a_n=2n-1. Find the smallest possible number of elements in the set {ai+aj∣0≤i≤j≤n}\{ a_i+a_j \mid 0\le i \le j \le n \}.
Plain-text mathematical notation (without MathML)
For a given integer n≥2, let a₀,a₁,…,a_(n) be integers satisfying 0=a₀<a₁<…<a_(n)=2n−1. Find the smallest possible number of elements in the set {a_(i)+a_(j)∣0≤i≤j≤n}.
Original LaTeX notation
For a given integer $n\ge 2$, let $a_0,a_1,\ldots ,a_n$ be integers satisfying $0=a_0<a_1<\ldots <a_n=2n-1$. Find the smallest possible number of elements in the set $\{ a_i+a_j \mid 0\le i \le j \le n \}$.

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Source and history

task_id
3191ff2a-47ac-5a01-a7b5-c6be16813981
task_key
test--3191ff2a-47ac-5a01-a7b5-c6be16813981
task_revision_id
5
config / split
/ test

Official source

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