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July 21st, 2009, 02:37 AM  #1 
Senior Member Joined: Apr 2007 Posts: 2,140 Thanks: 0  The 8th Korean Mathematical Olympiad
Since I'm Korean, I will post this interesting problem by KMO. 2. For a given positive integer , find all pairs of positive integers such that , are relatively prime and , where , , can be represented by functions of . 
July 22nd, 2009, 04:08 PM  #2 
Senior Member Joined: Apr 2007 Posts: 2,140 Thanks: 0  Re: The 8th Korean Mathematical Olympiad
Hint: this could require basic number theory knowledge.

July 22nd, 2009, 09:07 PM  #3  
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 931 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: The 8th Korean Mathematical Olympiad Quote:
 
July 22nd, 2009, 09:47 PM  #4  
Senior Member Joined: Apr 2007 Posts: 2,140 Thanks: 0  Re: The 8th Korean Mathematical Olympiad Quote:
 
July 23rd, 2009, 08:18 AM  #5  
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 931 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: The 8th Korean Mathematical Olympiad Quote:
 
July 23rd, 2009, 02:12 PM  #6  
Senior Member Joined: Apr 2007 Posts: 2,140 Thanks: 0  Re: The 8th Korean Mathematical Olympiad Quote:
 

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