Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


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

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

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
gus gassmann

Posts: 60
Registered: 7/26/12
Re: Reciprocals of integers summing to 1
Posted: Nov 16, 2012 9:57 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

On 16/11/2012 10:10 AM, redmond@siu.edu wrote:
> On Thursday, November 15, 2012 11:39:57 PM UTC-6, 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.
>>
>>
>>
>> C-B

>
> Here's another
>
> 1/2 + 1/3 + 1/7 + 1/42 = 1.
>
> don


What about 1/1 + 1/1 + 1/(-1)?

Seems to me that the original question was not very well stated.

Maybe you want x_i =/= x_j for i =/= j? That is still quite a bit more
work than I am willing to invest.

On the other hand,

M = {n | exist 0 < x_1 < x_2 < ... < x_n with sum 1/x_i = 1}

would be interesting. I offer k=2 as one positive integer that is not
contained in M. Are there others? Is there a nice characterization?




Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.