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Let A be a subset of {1, 2, 3 ... 2n-1, 2n} containing n + 1 elements Show that:

  • a) some two elements of a are relatively prime
  • b) some two elements of a have the property that one divides the other

I am assuming that we have to use the pigeon-hole principle here but I have no idea how to use it in this particular situation.

JMP
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Patrick Schick
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  • See https://math.stackexchange.com/questions/2818921/pigeonhole-principle-for-coprime-numbers and https://math.stackexchange.com/questions/3533489/pigeonhole-principle-for-numbers-and-their-divisors-within-a-set – player3236 Nov 20 '20 at 05:07
  • I got the $a$ part but how do you prove the $b$ part? – Patrick Schick Nov 20 '20 at 05:16
  • I linked two questions. Here is one more https://math.stackexchange.com/questions/315050/using-pigeonhole-principle-to-prove-two-numbers-in-a-subset-of-2n-divide-eac, and even more in the "linked questions" in that question. – player3236 Nov 20 '20 at 05:20

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