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#1 2006-08-02 18:38:55

krassi_holmz
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Registered: 2005-12-02
Posts: 1,908

Interesting identity

Prove that n is prime only and only when:

Expand the divisors and sum-of-divisors fuction as sums, which involve the floor function.

Make a function that using floors finds the i-th digit in the representation of n (for example demical representation)

What is the connection between the sum-of-digits function and the standard in the numberic theory

?

Last edited by krassi_holmz (2006-08-02 18:40:28)


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#2 2006-08-03 03:01:24

Ricky
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Registered: 2005-12-04
Posts: 3,791

Re: Interesting identity

Maybe I did my addition wrong, but:

Edit:

Now I'm confused about your wording.  You have "only and only when".  I took that as if and only if.  But did you mean that if the sum is 1, then n is prime?  In that case, 3 does not break your summation.


"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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#3 2006-08-03 04:04:03

krassi_holmz
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Registered: 2005-12-02
Posts: 1,908

Re: Interesting identity

Ricky wrote:

Maybe I did my addition wrong, but:

3/2???
Nooo...


The function floor is always integer, so you can't get rational result.
And yes, iff.

Last edited by krassi_holmz (2006-08-03 04:08:19)


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#4 2006-08-03 05:07:28

Ricky
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Registered: 2005-12-04
Posts: 3,791

Re: Interesting identity

Ah!!!  Floor.  I saw it, but didn't think about it.  That makes more sense now.


"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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#5 2006-08-03 05:09:45

Ricky
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Registered: 2005-12-04
Posts: 3,791

Re: Interesting identity

Not only that, krassi, but it appears that:

Where gd is the great divisor of n other than n itself.

Edit: Nevermind.  It doesn't work as sum(8) = 3

Edit #2: Where did you find this, and do you have such a proof?  If so, I'd like to see it.  Otherwise, I'll try to help you on it.


"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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#6 2006-08-03 05:30:14

krassi_holmz
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Registered: 2005-12-02
Posts: 1,908

Re: Interesting identity

It's very simple. And yes, it has connection to the d(x) and many more NT functions
I'll give you a hint: investigate the function:

Last edited by krassi_holmz (2006-08-03 05:47:54)


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#7 2006-08-03 05:52:20

krassi_holmz
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Registered: 2005-12-02
Posts: 1,908

Re: Interesting identity

In general,

Last edited by krassi_holmz (2006-08-03 05:55:06)


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#8 2006-08-03 05:57:06

krassi_holmz
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Registered: 2005-12-02
Posts: 1,908

Re: Interesting identity


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