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Omni-MATH / In the coordinate plane consider the set S of all points with integer coordinates. For a positive integer k, two distinct points A, B∈S will be called k-[i]friends[/i] if there is …

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problem

In the coordinate plane consider the set S S of all points with integer coordinates. For a positive integer k k, two distinct points AA, B∈S B\in S will be called k k-[i]friends[/i] if there is a point C∈S C\in S such that the area of the triangle ABC ABC is equal to k k. A set T⊂S T\subset S will be called k k-[i]clique[/i] if every two points in T T are k k-friends. Find the least positive integer k k for which there exits a k k-clique with more than 200 elements. [i]
Plain-text mathematical notation (without MathML)
In the coordinate plane consider the set S of all points with integer coordinates. For a positive integer k, two distinct points A, B∈S will be called k-[i]friends[/i] if there is a point C∈S such that the area of the triangle ABC is equal to k. A set T⊂S will be called k-[i]clique[/i] if every two points in T are k-friends. Find the least positive integer k for which there exits a k-clique with more than 200 elements.

[i]
Original LaTeX notation
In the coordinate plane consider the set $ S$ of all points with integer coordinates. For a positive integer $ k$, two distinct points $A$, $ B\in S$ will be called $ k$-[i]friends[/i] if there is a point $ C\in S$ such that the area of the triangle $ ABC$ is equal to $ k$. A set $ T\subset S$ will be called $ k$-[i]clique[/i] if every two points in $ T$ are $ k$-friends. Find the least positive integer $ k$ for which there exits a $ k$-clique with more than 200 elements.

[i]

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Source and history

task_id
b26a436e-8659-5ba7-b5fb-0a5ef5a7ffe5
task_key
test--b26a436e-8659-5ba7-b5fb-0a5ef5a7ffe5
task_revision_id
1
config / split
/ test

Official source

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