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September 1st, 2009, 01:56 AM   #1
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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
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September 2nd, 2009, 08:55 AM   #2
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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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