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Omni-MATH / Find the smallest positive integer n such that if n squares of a 1000×1000 chessboard are colored, then there will exist three colored squares whose centers form a right triangle w…

Problem

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problem

Find the smallest positive integer nn such that if nn squares of a 1000×10001000 \times 1000 chessboard are colored, then there will exist three colored squares whose centers form a right triangle with sides parallel to the edges of the board.
Plain-text mathematical notation (without MathML)
Find the smallest positive integer  n such that if n squares of a 1000×1000 chessboard are colored, then there will exist three colored squares whose centers form a right triangle with sides parallel to the edges of the board.
Original LaTeX notation
Find the smallest positive integer  $n$ such that if $n$ squares of a $1000 \times 1000$ chessboard are colored, then there will exist three colored squares whose centers form a right triangle with sides parallel to the edges of the board.

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Source and history

task_id
89ea1834-d605-5a8d-be84-eae72a9689f6
task_key
test--89ea1834-d605-5a8d-be84-eae72a9689f6
task_revision_id
1
config / split
/ test

Official source

initial import