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 [SOLVED] Number theory

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Mohammad
Descartes
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[SOLVED] Number theory Empty
PostSubject: [SOLVED] Number theory   [SOLVED] Number theory EmptySun Nov 08, 2009 12:51 pm

Basketball
Here is an easy problem in number theory,my favorite part of mathematics,
uploading.com Number%2Btheory.pdf/ bounce
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Bruno
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Bruno

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[SOLVED] Number theory Empty
PostSubject: Re: [SOLVED] Number theory   [SOLVED] Number theory EmptySun Nov 08, 2009 1:38 pm

What about 2? One of A,B must contain 1 (say A), and then A+A contains 2...
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peyman
Euclid
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peyman

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PostSubject: Re: [SOLVED] Number theory   [SOLVED] Number theory EmptySun Nov 08, 2009 2:30 pm

Mohammad wrote:
Basketball
Here is an easy problem in number theory,my favorite part of mathematics,
uploading.com Number%2Btheory.pdf/ bounce

waiting 60 seconds Sleep
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Mohammad
Descartes
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Mohammad

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PostSubject: Re: [SOLVED] Number theory   [SOLVED] Number theory EmptySun Nov 08, 2009 9:29 pm

forget about 1+1=2 Very Happy
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Bruno
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PostSubject: Re: [SOLVED] Number theory   [SOLVED] Number theory EmptySun Nov 08, 2009 11:04 pm

Hello!
Here is my solution. cat
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Mohammad
Descartes
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Mohammad

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PostSubject: Re: [SOLVED] Number theory   [SOLVED] Number theory EmptySun Nov 08, 2009 11:08 pm

Perfect, well done! bounce
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Mohammad
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PostSubject: Generalization   [SOLVED] Number theory EmptySun Nov 08, 2009 11:32 pm

Generalization

For n=2k k\ge 1, of course the obvious candidate is not unique. Simply for example take n=4k with x\in P_{4k} and y\in P_{4k+2}. Another partitioning is P_{4k}-x\cup {y}, P_{4k+2}-y\cup {x}, so you can exchange every two numbers and get new partitioning, so no uniqueness and actually infinite numbers of partitioning. bounce
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PostSubject: Re: [SOLVED] Number theory   [SOLVED] Number theory EmptyMon Nov 09, 2009 12:13 am

Good! afro
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