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

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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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,532

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

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

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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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,532

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

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

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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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...

Please give an example

'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'

'Humanity is still kept intact. It remains within.' -Alokananda

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,776

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.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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