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**Mathegocart****Member**- Registered: 2012-04-29
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1.Express

as the product of 2 factors, where neither of them is 1.

2. Express as the product of 2 factors, where neither of them is 1. Do not express these 2 factors explicitly.

3. What does equal?

4. Find all integers where n! is a multiple of n^2.

5. If 3 numbers are chosen at random from first 1000 natural numbers,what is the probability that the three numbers are in G.P.? All numbers are distinct.

6. prove that is true for all non negative integers.

*Last edited by Mathegocart (2016-07-21 02:09:08)*

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**bobbym****bumpkin**- From: Bumpkinland
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Hi;

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**Mathegocart****Member**- Registered: 2012-04-29
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bobbym wrote:

Hi;

Correct.

The integral of hope is reality.

May bobbym have a wonderful time in the pearly gates of heaven.

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
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Hi;

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**thickhead****Member**- Registered: 2016-04-16
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*Last edited by thickhead (2016-07-20 04:05:57)*

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**thickhead****Member**- Registered: 2016-04-16
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**{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha{Gods rejoice at those places where ladies are respected.}**

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**Mathegocart****Member**- Registered: 2012-04-29
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thickhead wrote:

Thickhead, could you explain the process on the inequality? I used a bit of Cauchy Schwarz on this.

*Last edited by Mathegocart (2016-07-21 02:08:44)*

The integral of hope is reality.

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He will be sorely missed.

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**Mathegocart****Member**- Registered: 2012-04-29
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bobbym wrote:

Hi;

Both answers are reasonable solutions, also thickhead has a good soultion as well.

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**Mathegocart****Member**- Registered: 2012-04-29
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thickhead wrote:

6 also is a solution, and 6 is not a cube. = 20

*Last edited by Mathegocart (2016-07-21 02:12:49)*

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**thickhead****Member**- Registered: 2016-04-16
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Mathegocart wrote:

thickhead wrote:6 also is a solution, and 6 is not a cube. http://latex.codecogs.com/gif.latex?%5Cfrac%7B6%21%7D%7B6%5E%7B2%7D%7D = 20

I just wrote offhand. I had an obvious flash about cubes.Unless n is specified it becomes difficult to make exhaustive list.

**{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha{Gods rejoice at those places where ladies are respected.}**

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Hi;

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**thickhead****Member**- Registered: 2016-04-16
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bobbym is right. I had not thought properly.After knowing it it looks very simple. A composite number means at least two factors which make up for one "n" the other n being provided by the number itself. Perhaps I tried 4 and seeing it not correct went for 8 and made it a cube. Very unscientific thinking on my part.

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**thickhead****Member**- Registered: 2016-04-16
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*Last edited by thickhead (2016-07-24 23:20:14)*

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**thickhead****Member**- Registered: 2016-04-16
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*Last edited by thickhead (2016-07-25 15:28:10)*

(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha

{Gods rejoice at those places where ladies are respected.}

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**thickhead****Member**- Registered: 2016-04-16
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Why is Mathegocart silent ?Is he too busy with other problems? One more thing instead of G.P. if the 3 numbers are in A.P. what is the probability for first 1000 natural numbers or even first n natural numbers?

(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha

{Gods rejoice at those places where ladies are respected.}

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Hi;

f the 3 numbers are in A.P. what is the probability for first n natural numbers?

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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*Last edited by zetafunc (2016-07-27 05:02:26)*

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**thickhead****Member**- Registered: 2016-04-16
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(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha

{Gods rejoice at those places where ladies are respected.}

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

You are correct, further simplification is possible. Normally, I do not automatically simplify all the way. There are good reasons for this but in this case they do not apply, further simplification was called for.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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