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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: 15,919

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

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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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**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: 15,919

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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**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

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'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 94,455

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.**

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