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## #1 2016-07-19 07:20:45

Mathegocart
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Registered: 2012-04-29
Posts: 1,882

### Exponent Slash, #1

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)

The integral of hope is reality.

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## #2 2016-07-19 09:27:01

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

### Re: Exponent Slash, #1

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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## #3 2016-07-19 09:55:12

Mathegocart
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Registered: 2012-04-29
Posts: 1,882

### Re: Exponent Slash, #1

bobbym wrote:

Hi;

Correct.

The integral of hope is reality.

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## #4 2016-07-19 12:59:29

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

### Re: Exponent Slash, #1

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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## #5 2016-07-19 16:14:30

Member
Registered: 2016-04-16
Posts: 1,086

### Re: Exponent Slash, #1

The answer is not unique. There are 63 different ways.

Last edited by thickhead (2016-07-20 04:05:57)

{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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## #6 2016-07-19 16:22:11

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Registered: 2016-04-16
Posts: 1,086

### Re: Exponent Slash, #1

{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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## #7 2016-07-21 02:07:08

Mathegocart
Member
Registered: 2012-04-29
Posts: 1,882

### Re: Exponent Slash, #1

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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## #8 2016-07-21 02:10:10

Mathegocart
Member
Registered: 2012-04-29
Posts: 1,882

### Re: Exponent Slash, #1

bobbym wrote:

Hi;

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

The integral of hope is reality.

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## #9 2016-07-21 02:12:24

Mathegocart
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Registered: 2012-04-29
Posts: 1,882

### Re: Exponent Slash, #1

6 also is a solution, and 6 is not a cube. $\frac{6!}{6^{2}}$ = 20

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

The integral of hope is reality.

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## #10 2016-07-21 02:46:10

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Registered: 2016-04-16
Posts: 1,086

### Re: Exponent Slash, #1

Mathegocart 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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## #11 2016-07-21 02:52:50

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

### Re: Exponent Slash, #1

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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## #12 2016-07-21 03:47:12

Member
Registered: 2016-04-16
Posts: 1,086

### Re: Exponent Slash, #1

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.

{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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## #13 2016-07-24 22:41:11

Member
Registered: 2016-04-16
Posts: 1,086

### Re: Exponent Slash, #1

Last edited by thickhead (2016-07-24 23:20:14)

{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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## #14 2016-07-25 04:51:22

Member
Registered: 2016-04-16
Posts: 1,086

### Re: Exponent Slash, #1

Last edited by thickhead (2016-07-25 15:28:10)

{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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## #15 2016-07-26 23:57:50

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Registered: 2016-04-16
Posts: 1,086

### Re: Exponent Slash, #1

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?

{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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## #16 2016-07-27 01:40:23

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

### Re: Exponent Slash, #1

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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## #17 2016-07-27 03:27:15

zetafunc
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Registered: 2014-05-21
Posts: 2,109
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### Re: Exponent Slash, #1

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

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## #18 2016-07-27 04:02:20

Member
Registered: 2016-04-16
Posts: 1,086

### Re: Exponent Slash, #1

{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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## #19 2016-07-27 06:05:17

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

### Re: Exponent Slash, #1

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.

Offline