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Omni-MATH / Find the smallest positive integer K such that every K-element subset of {1,2,...,50} contains two distinct elements a,b such that aplus{}b divides ab.

Problem

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problem

Find the smallest positive integer

K

such that every

K

-element subset of

\{1,2,...,50 \}

contains two distinct elements

a,b

such that $ a\plus{}b$ divides

ab

Plain-text mathematical notation (without MathML)

Find the smallest positive integer K such that every K-element subset of {1,2,...,50} contains two distinct elements a,b such that $ a\plus{}b$ divides ab.

Original LaTeX notation

Find the smallest positive integer $ K$ such that every $ K$-element subset of $ \{1,2,...,50 \}$ contains two distinct elements $ a,b$ such that $ a\plus{}b$ divides $ ab$.

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task_id: 4b796d31-eb0b-5b19-9cb7-3cec88647269
task_key: test--4b796d31-eb0b-5b19-9cb7-3cec88647269
task_revision_id: 3
config / split: / test

Official source

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