Math Is Fun Forum
  Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

You are not logged in.

#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.

Offline

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

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,886

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

Offline

#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.

Offline

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

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,886

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

Offline

#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

Offline

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

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 15,356
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...

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

Offline

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

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 83,211

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 have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

Board footer

Powered by FluxBB