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

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 Charlie-Boo Posts: 1,635 Registered: 2/27/06
Re: Reciprocals of integers summing to 1
Posted: Nov 17, 2012 4:19 PM
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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

Date Subject Author
11/16/12 Charlie-Boo
11/16/12 William Elliot
11/16/12 Charlie-Boo
11/16/12 William Elliot
11/17/12 Charlie-Boo
11/18/12 Bill Taylor
11/21/12 David Petry
11/22/12 Bill Taylor
11/22/12 Luis A. Rodriguez
11/22/12 David Petry
11/22/12 David Petry
11/23/12 Bill Taylor
11/23/12
11/23/12 Bill Taylor
11/16/12 Don Redmond
11/16/12 gus gassmann
11/16/12 billh04
11/17/12 Luis A. Rodriguez
11/17/12 Charlie-Boo
11/19/12 Luis A. Rodriguez
11/20/12 doumin
11/22/12 Bill Taylor

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