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I'm supposed to prove the theorem in the title for a combinatorics class (continuation of discrete structures class). At the moment I have no idea how to aproach this question.

I would appreciate some pointers to set me on the right path. I don't really want to just copy a full solution and hand it over as mine.

Any help will be greatly appreciated.

Mr Redstoner
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1 Answers1

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Hints:

  1. Prove this for prime powers first. (you will have to use a little trick to to extend this to all natural numbers and ensure that the digits remain $0$s and $1$s)
  2. Consider all numbers with digits $0$s and $1$s. Apply the pigeonhole principle.

I hope this is helpful! Feel free to ask for further clarification.

vxnture
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  • Thanks for the pigeonhole one. That sounds much like the expected solution by what was in the class. Would upvote if I had enough rep. – Mr Redstoner Mar 17 '19 at 09:09