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## #1 2012-12-26 08:39:41

pellerinb
Member
Registered: 2012-12-26
Posts: 43

### n! = ...

Can any n! be represented by a sum of natural numbers {a[1], a[2], a[3] ...} raised to any power such that a[i] ≠ a[j] and 0 < a[i],a[j] <= n for all i and j?

1! = 1
2! = 2
3! = 3 + 2 + 1
4! = 4^2 + 3 + 2^2 + 1
5! = 5^2 + 4^3 + 3^3 + 2^2
6! = 5^4 + 4^3 + 3^3 + 2^2

Who knows?  :)

Last edited by pellerinb (2012-12-26 08:42:02)

Prime numbers have got to be the neatest things; they are like atoms. Composites are two or more primes held together by multiplication.
In biology, we use math like we know what we are talking about. Sad isn't it.

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## #2 2012-12-26 08:41:20

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,037

### Re: n! = ...

They can. Just pad it up with 1's.

Here lies the reader who will never open this book. He is forever dead.
Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

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## #3 2012-12-26 08:42:34

pellerinb
Member
Registered: 2012-12-26
Posts: 43

### Re: n! = ...

hense the edit, anonimnystefy.

Prime numbers have got to be the neatest things; they are like atoms. Composites are two or more primes held together by multiplication.
In biology, we use math like we know what we are talking about. Sad isn't it.

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## #4 2012-12-26 08:45:20

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,037

### Re: n! = ...

I think all numbers can be represented that way, not only factorials... But that is just a conjecture, I do not have a proof...

Here lies the reader who will never open this book. He is forever dead.
Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

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## #5 2013-01-22 02:26:34

n872yt3r
Member
Registered: 2013-01-21
Posts: 392

### Re: n! = ...

I need to know the pattern for n! because I am so confused.

- n872yt3r
Math Is Fun Rocks!
By the power of the exponent, I square and cube you!

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## #6 2013-01-22 03:13:17

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,835
Website

### Re: n! = ...

anonimnystefy wrote:

I think all numbers can be represented that way, not only factorials... But that is just a conjecture, I do not have a proof...

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

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## #7 2013-01-22 03:27:04

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

### Re: n! = ...

He is representing factorials. The question does not seem to make sense for other 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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