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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
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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
,where sigma is the sum of the xth powers of all divisors of n.
IPBLE: Increasing Performance By Lowering Expectations.