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#26 2012-12-25 23:00:06

anonimnystefy
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From: The Foundation
Registered: 2011-05-23
Posts: 15,544

Re: A nice diophantine equation.

It doesn't!


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#27 2012-12-25 23:06:42

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 87,237

Re: A nice diophantine equation.

Hi;

The gf does not look like the right form to use that formula.


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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#28 2012-12-25 23:17:22

anonimnystefy
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Registered: 2011-05-23
Posts: 15,544

Re: A nice diophantine equation.

It is in the right form.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#29 2012-12-25 23:18:46

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 87,237

Re: A nice diophantine equation.

Hmmmm. Then how do you account for the fact that it does not get a good answer?


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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#30 2012-12-25 23:21:11

anonimnystefy
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From: The Foundation
Registered: 2011-05-23
Posts: 15,544

Re: A nice diophantine equation.

Well, it is an approximation formula... It does no guarantee a close approximation...


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#31 2012-12-25 23:24:05

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 87,237

Re: A nice diophantine equation.

Hi;

That is not correct. The limit of that approximation  divided by the exact answer
should approach 1 as n approaches infinity.


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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#32 2012-12-25 23:27:40

anonimnystefy
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From: The Foundation
Registered: 2011-05-23
Posts: 15,544

Re: A nice diophantine equation.

It should. But, does it?


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#33 2012-12-25 23:39:54

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,237

Re: A nice diophantine equation.

Hi;

I think this gf

is not in the right form. Look at the formula,

it can not deal with 3 different terms in the denominator. That is why it is not working.


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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#34 2012-12-26 06:29:32

anonimnystefy
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From: The Foundation
Registered: 2011-05-23
Posts: 15,544

Re: A nice diophantine equation.

You can factorise the denominator. You'll have three (1-x) terms. The rest goes into B(x).

And you have copied the required form incorrectly...

Last edited by anonimnystefy (2012-12-26 06:30:39)


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#35 2012-12-26 06:34:50

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,237

Re: A nice diophantine equation.

Hi;

Are you sure that is not the required form?


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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#36 2012-12-26 06:37:41

anonimnystefy
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From: The Foundation
Registered: 2011-05-23
Posts: 15,544

Re: A nice diophantine equation.

Yes. But, in either case, A(x) will be the zero polynomial, so they come down to the same thing.

Look at the wiki article to see the correct form.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#37 2012-12-26 06:38:53

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 87,237

Re: A nice diophantine equation.

I can not split that generating function into what you want. Can you show what you did?

The form I have is correct.

See this page

http://en.wikipedia.org/wiki/Generating_function


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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#38 2012-12-26 06:50:41

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,544

Re: A nice diophantine equation.

Those two are not the same...


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#39 2012-12-26 06:52:48

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,237

Re: A nice diophantine equation.

Hi;

Yes, you are right! I see that. Very good. But I still think I have you on the gf.

I say that you will be unable to split it as you say.


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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#40 2012-12-26 07:19:39

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,544

Re: A nice diophantine equation.

Hi bobbym

Now we have α=1, β=3, A(x)=0, r=1,

Last edited by anonimnystefy (2012-12-26 07:28:09)


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#41 2012-12-26 07:22:02

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,237

Re: A nice diophantine equation.

Hi;

I do not think you can do that with B(x).


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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#42 2012-12-26 07:24:50

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,544

Re: A nice diophantine equation.

Why not? It is analytic...


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#43 2012-12-26 07:26:05

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,237

Re: A nice diophantine equation.

When you put that into B(x) you will not get the original gf back.


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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#44 2012-12-26 07:27:19

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,544

Re: A nice diophantine equation.

I do not understand you...


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#45 2012-12-26 07:33:07

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,237

Re: A nice diophantine equation.

See what you put into B(x) it does not equal the original generating function. What is in the denominator of your B(x) does not get to the the denominator of the asymptotic form.


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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#46 2012-12-26 07:34:37

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,544

Re: A nice diophantine equation.

Hi bobbym

You didn't substitute the rest of the parameters. α=0, β=3, A(x)=0, r=1.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#47 2012-12-26 07:39:57

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,237

Re: A nice diophantine equation.

Hi;

But something is wrong. If you are right you should have got a better answer than you did. I do not understand what is going wrong. I am rechecking everything please hold.

When I make your substitutions I get


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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#48 2012-12-26 07:50:39

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,544

Re: A nice diophantine equation.

Hi bobbym

Where do you get the x from?


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#49 2012-12-26 07:55:10

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,237

Re: A nice diophantine equation.

That problem is solved I had alpha as 1 instead of 0. Your form is right.


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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#50 2012-12-26 08:07:57

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,544

Re: A nice diophantine equation.

But, with α=0 that will just vanish...


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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