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September 1st, 2009, 01:56 AM  #1 
Senior Member Joined: Apr 2007 Posts: 2,140 Thanks: 0  A problem from 32nd International Mathematical Olympiad
2. Let be an integer and be all the natural numbers less than and relatively prime to If prove that must be either a prime number or a power of 
September 2nd, 2009, 08:55 AM  #2 
Senior Member Joined: Dec 2008 Posts: 160 Thanks: 0  Re: A problem from 32nd International Mathematical Olympiad
Clearly, form arithmetical progression with as base and fixed If  prime,  set of all numbers < n. If  set of all odd numbers < n If n has prime divider other than 2  progression should have a 'dents'  numbers that multiple that prime divider, that is impossible, because, otherwise, it will not cover all numbers < n. Like: should not belong to the set, while for some k should. 

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