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**krassi_holmz****Real Member**- Registered: 2005-12-02
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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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**Ricky****Moderator**- Registered: 2005-12-04
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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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**krassi_holmz****Real Member**- Registered: 2005-12-02
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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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**Ricky****Moderator**- Registered: 2005-12-04
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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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**Ricky****Moderator**- Registered: 2005-12-04
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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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**krassi_holmz****Real Member**- Registered: 2005-12-02
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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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**krassi_holmz****Real Member**- Registered: 2005-12-02
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In general,

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

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**krassi_holmz****Real Member**- Registered: 2005-12-02
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,where sigma is the sum of the xth powers of all divisors of n.

IPBLE: Increasing Performance By Lowering Expectations.

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