Combinatorics · Counterexamples · Coprimality · Ramsey type statements · Extremal constructions
Prove or disprove the following assertion.
Among any six positive integers it is always possible to choose three of them that are pairwise coprime, or three of them that have a common divisor greater than \(1\).
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Serbian Municipal Competition 2005, high school grade I, category A, problem 5. Organized by the Mathematical Society of Serbia (DMS). Source