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#1 2012-12-27 07:39:41

pellerinb
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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 (2012-12-27 07:42:02)

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.

#2 2012-12-27 07:41:20

anonimnystefy
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Re: n! = ...

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

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#3 2012-12-27 07:42:34

pellerinb
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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.

#4 2012-12-27 07:45:20

anonimnystefy
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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...

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#5 2013-01-23 01:26:34

n872yt3r
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Re: n! = ...

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!

#6 2013-01-23 02:13:17

Agnishom
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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...

'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'
'Who are you to judge everything?' -Alokananda

#7 2013-01-23 02:27:04

bobbym

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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.