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Topic: Integer pairs in sum of reciprocals
Replies: 39   Last Post: Jan 22, 2001 6:02 PM

 Messages: [ Previous | Next ]
 Ross A. Finlayson Posts: 2,055 Registered: 12/13/04
Re: Integer pairs in sum of reciprocals
Posted: Jan 1, 2001 10:00 PM

saxon970@yahoo.com wrote:

> Hello. I have some questions about how to approach the problem below:
>
> How many pairs of positive integers a and b are there such that a < b
> and
> 1/a + 1/b = 1/2001 ?
>
> End of problem.
>
> Is trial and error and making a manual list the way to go?
>
> Thanks.
>
> Sent via Deja.com
> http://www.deja.com/

Set a to 2001 or greater and b to a large value. The result is very close
to 1/2001, where 2001 is called c,

1/a + 1/b = 1/c, or

a ^-1 + b ^-1 = c^-1

There are probably infinite solutions.

Ross

--
Ross Andrew Finlayson
Finlayson Consulting
Ross at Tiki-Lounge: http://www.tiki-lounge.com/~raf/
"The best mathematician in the world is Maplev in Ontario." - Pertti L.