Math Is Fun Forum

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)

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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.

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: n! = ...

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

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“Here lies the reader who will never open this book. He is forever dead.
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pellerinb

Member

Registered: 2012-12-26

Posts: 43

Re: n! = ...

hense the edit, anonimnystefy.

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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.

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

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...

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“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.

n872yt3r

Member

Registered: 2013-01-21

Posts: 392

Re: n! = ...

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

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

Agnishom

Real Member

From: Riemann Sphere

Registered: 2011-01-29

Posts: 24,996

Website

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...

Please give an example

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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.

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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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