For the math geeks

[Bob78164]

Let n be a positive integer. Choose at least n + 1 positive integers between 1 and 2n, inclusive. Prove that at least one of your choices must be an integer multiple of another of your choices (or put another way, prove that one of your choices must exactly divide another of your choices).

So, for example, no matter which 101 integers you choose between 1 and 200, inclusive, one of your choices must divide another.

I'm asking this because my son, taking his first proof-based math course in his sophomore year last year, eventually (a week after the assignment was due) solved it and I'm pretty impressed with the insight he employed to come up with his proof.

Have fun! --Bob