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#51 2012-12-01 20:09:39

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 85,347

Re: Number Theory

Hi;

1 x 2 x 3 x 4 x 5 x 6 x ... x 55

Is less than

100 x 100 x 100 x 100 x 100 x100 x ... x 100

So 55! is less than 10^110. This is a rough upper bound.


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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#52 2012-12-01 20:36:11

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 85,347

Re: Number Theory

Hi;

Is that the answer for K, then what is P?


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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#53 2012-12-01 21:00:41

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 85,347

Re: Number Theory

Hi;

Yes, that 103 is correct. You can do it by the number of trailing zeroes of a factorial.


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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#54 2012-12-01 21:21:04

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 85,347

Re: Number Theory

Hi;

I have a formula that is close but not yet exact, I will work on it and post when I get it.


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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#55 2012-12-01 21:30:27

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 85,347

Re: Number Theory

Hi;

One question at a time. The answer I believe for the factorial problem.

1) Compute the highest power of 2 in 10000! which is 9995.

2) Compute the highest power of 2 in 100! which is 97

3) Divide 9995 by 97 and take the floor value. You get 103.


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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#56 2012-12-01 21:43:24

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 85,347

Re: Number Theory

The highest power gives 104 which is one too many. The smallest power seems to give the right answer. I am not sure why but it is working.

For instance:

It gets k = 1030 which is correct.


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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#57 2012-12-01 22:05:10

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 85,347

Re: Number Theory

1030 is correct for 100000!. 103 is correct for 10000!.


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.

Offline

#58 2012-12-01 22:17:24

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 85,347

Re: Number Theory

No problem. Please post your remaining questions in Help me. Start a new thread there, this thread belongs to Ganesh's questions.


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.

Offline

#59 2012-12-01 23:03:14

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 85,347

Re: Number Theory

Hi;

You can not post a link until you have been here a while. Open up a new thread and I will fill in the link.


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.

Offline

#60 2012-12-01 23:13:48

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 85,347

Re: Number Theory

That is what you use, post new topic. Press that and you be able to post 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.

Offline

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