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Omni-MATH / Let S be a subset of the set {1,2,3,…,2015} such that for any two elements a,b∈S, the difference a−b does not divide the sum a+b. Find the maximum possible size of S.

Problem

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problem

Let SS be a subset of the set {1,2,3,…,2015}\{1,2,3, \ldots, 2015\} such that for any two elements a,b∈Sa, b \in S, the difference a−ba-b does not divide the sum a+ba+b. Find the maximum possible size of SS.
Plain-text mathematical notation (without MathML)
Let S be a subset of the set {1,2,3,…,2015} such that for any two elements a,b∈S, the difference a−b does not divide the sum a+b. Find the maximum possible size of S.
Original LaTeX notation
Let $S$ be a subset of the set $\{1,2,3, \ldots, 2015\}$ such that for any two elements $a, b \in S$, the difference $a-b$ does not divide the sum $a+b$. Find the maximum possible size of $S$.

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Source and history

task_id
9af14814-af0f-599c-8258-6475bde06ae6
task_key
test--9af14814-af0f-599c-8258-6475bde06ae6
task_revision_id
1
config / split
/ test

Official source

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