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#1 2006-08-03 16:38:55

krassi_holmz
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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 (2006-08-03 16:40:28)


IPBLE:  Increasing Performance By Lowering Expectations.
 

#2 2006-08-04 01:01:24

Ricky
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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..."
 

#3 2006-08-04 02:04:03

krassi_holmz
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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 (2006-08-04 02:08:19)


IPBLE:  Increasing Performance By Lowering Expectations.
 

#4 2006-08-04 03:07:28

Ricky
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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..."
 

#5 2006-08-04 03:09:45

Ricky
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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..."
 

#6 2006-08-04 03:30:14

krassi_holmz
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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 (2006-08-04 03:47:54)


IPBLE:  Increasing Performance By Lowering Expectations.
 

#7 2006-08-04 03:52:20

krassi_holmz
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Re: Interesting identity

In general,

Last edited by krassi_holmz (2006-08-04 03:55:06)


IPBLE:  Increasing Performance By Lowering Expectations.
 

#8 2006-08-04 03:57:06

krassi_holmz
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Re: Interesting identity


IPBLE:  Increasing Performance By Lowering Expectations.
 

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