# Primes

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• Oct 16th 2009, 08:15 AM
usagi_killer
Primes
Prove that if one chooses more than n numbers from the set http://stuff.daniel15.com/cgi-bin/ma...202n%5Crbrace, then two of them are relatively prime.
• Oct 16th 2009, 09:13 AM
Bruno J.
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.