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#1 2013-09-29 05:36:15

jacks
Member
Registered: 2012-11-21
Posts: 80

positive integer ordered pairs (n,r)

{A} Total no. of positive integer ordered pairs of

which satisfy

{B} Total no. of positive integer ordered pairs of

which satisfy

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#2 2013-09-29 06:44:11

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,258

Re: positive integer ordered pairs (n,r)

Hi;

There are 6 ways for 120 and 2 ways for 2013.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#3 2013-09-29 06:46:32

jacks
Member
Registered: 2012-11-21
Posts: 80

Re: positive integer ordered pairs (n,r)

Thanks Bobbym would you like to explain it to me, Thanks

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#4 2013-09-29 06:52:38

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,258

Re: positive integer ordered pairs (n,r)

Hi;

As far as I know there is no known formula for these problems. The latest work only provides a bound, not an exact answer. These had to be computed for both numbers.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#5 2013-09-29 06:55:30

jacks
Member
Registered: 2012-11-21
Posts: 80

Re: positive integer ordered pairs (n,r)

Yes Bobbym I need upper bond.

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#6 2013-09-29 07:07:02

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,258

Re: positive integer ordered pairs (n,r)

Hi;

Unless I am misunderstanding their paper they have only established an upper bound for

n >= 2r

this is almost useless for your question.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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