olymmath

JBMO-SL 2019 C1

    Let SS be a set of 100 positive integers having the following property:

    "Among every four numbers of SS, there is a number which divides each of the other three or there is a number which is equal to the sum of the other three."

    Prove that the set SS contains a number which divides each of the other 99 numbers of SS.

    Dataset text NuminaMath olympiads. Quoted with source.

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