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Math Help - Primes

  1. #1
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    Primes

    Prove that if one chooses more than n numbers from the set then two of them are relatively prime.
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  2. #2
    MHF Contributor Bruno J.'s Avatar
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    Partition them as \{1,2\},\ \{3,4\},\ \hdots,\{2n-1,2n\}. Since there are n parts, one part must contain two of the numbers, and hence two of the numbers are adjacent. Since adjacent numbers are relatively prime we are done.
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