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July 21st, 2009, 02:37 AM   #1
 
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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 .
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July 22nd, 2009, 04:08 PM   #2
 
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Re: The 8th Korean Mathematical Olympiad

Hint: this could require basic number theory knowledge.
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July 22nd, 2009, 09:07 PM   #3
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Re: The 8th Korean Mathematical Olympiad

Quote:
Originally Posted by johnny
where , , can be represented by functions of .
What does this mean?
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July 22nd, 2009, 09:47 PM   #4
 
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Re: The 8th Korean Mathematical Olympiad

Quote:
Originally Posted by CRGreathouse
Quote:
Originally Posted by johnny
where , , can be represented by functions of .
What does this mean?
For example, m(x) = n+x+y?
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July 23rd, 2009, 08:18 AM   #5
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Re: The 8th Korean Mathematical Olympiad

Quote:
Originally Posted by johnny
For example, m(x) = n+x+y?
So "where n, x, y can be represented by functions of m" means "m is a function of n, x, and y"?
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July 23rd, 2009, 02:12 PM   #6
 
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Re: The 8th Korean Mathematical Olympiad

Quote:
Originally Posted by CRGreathouse
Quote:
Originally Posted by johnny
For example, m(x) = n+x+y?
So "where n, x, y can be represented by functions of m" means "m is a function of n, x, and y"?
I think so, but I'm 75% sure about it.
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