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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: The Foundation
Registered: 2011-05-23
Posts: 15,657

Re: n! = ...

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


“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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#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: The Foundation
Registered: 2011-05-23
Posts: 15,657

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

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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. eek what


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

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

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 18,862
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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...

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'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

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

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,600

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.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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