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My son, a sophomore in college taking his first proof-based course, was able to prove the following. I was both impressed and proud of him. Can you prove this statement?

Choose n+1 positive integers, all of them less than or equal to 2n. Prove that at least one of your choices must divide another of your choices.

It's easy to see that n integers isn't sufficient. Make your choices all of the numbers from n+1 to 2n, and none of your choices divide any of the others. But can you prove that any set of n+1 choices must contain a pair, one of which divides the other? --Bob
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