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Math Forum » Discussions » sci.math.* » sci.math.independent

Topic: Reciprocals of integers summing to 1
Replies: 21   Last Post: Nov 23, 2012 8:44 PM

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Charlie-Boo

Posts: 1,569
Registered: 2/27/06
Re: Reciprocals of integers summing to 1
Posted: Nov 17, 2012 4:19 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

On Nov 16, 2:52 am, William Elliot <ma...@panix.com> wrote:
> On Thu, 15 Nov 2012, Charlie-Boo wrote:
> > On Nov 16, 12:21 am, William Elliot <ma...@panix.com> wrote:
> > > On Thu, 15 Nov 2012, Charlie-Boo wrote:
> > > > For each n, what are the solutions in positive integers (or in
> > > > integers) to (1/X1)+(1/X2) + . . . + (1/Xn)=1 ?
>
> > > x1 = x2 =..= x_n = n
>
> > But there is also 1/2 + 1/3 + 1/6 = 1.  I am asking for all solutions.
>
> 1/3 + 1/2 + 1/6
> 1/6 + 1/3 + 1/2,
> etc.,
> for a total of 6 + 1.
>
> Do I hear more?
>
>

Start with {1}, a set containing N elements including N! . Replace N!
with (N+1)!/N and (N+1)! to create another such set.

C-B

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