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

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Brian Evans

Posts: 5
Registered: 12/8/04
Re: Integer pairs in sum of reciprocals
Posted: Jan 4, 2001 2:29 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply



From what I can deduce the answer is actually none.

Starting at the boundary condition for where a= b :
1/4002 + 1/4002 = 1/2001
Which reduces to
1/2 + 1/2 = 1
Now for us to move off the boundary condition one
of these must grow and the other shrink. Problem
is there is no 1/x greater than 1/2 so one can not
get any bigger.

Brian Evans

<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?









Date Subject Author
1/1/01
Read Integer pairs in sum of reciprocals
saxon970@yahoo.com
1/1/01
Read Re: Integer pairs in sum of reciprocals
Ross A. Finlayson
1/2/01
Read Re: Integer pairs in sum of reciprocals
Ross A. Finlayson
1/2/01
Read Re: Integer pairs in sum of reciprocals
Jan Kristian Haugland
1/2/01
Read Re: Integer pairs in sum of reciprocals
Ross A. Finlayson
1/2/01
Read Re: Integer pairs in sum of reciprocals
Jan Kristian Haugland
1/2/01
Read Re: Integer pairs in sum of reciprocals
Ross A. Finlayson
1/2/01
Read Re: Integer pairs in sum of reciprocals
Steve Lord
1/2/01
Read Re: Integer pairs in sum of reciprocals
Ross A. Finlayson
1/2/01
Read Re: Integer pairs in sum of reciprocals
Ross A. Finlayson
1/2/01
Read Re: Integer pairs in sum of reciprocals
Dik T. Winter
1/3/01
Read Re: Integer pairs in sum of reciprocals
Philip Anderson
1/11/01
Read Re: Integer pairs in sum of reciprocals
355113@my-deja.com
1/1/01
Read Re: Integer pairs in sum of reciprocals
David Eppstein
1/2/01
Read Re: Integer pairs in sum of reciprocals
r.e.s.
1/2/01
Read Re: Integer pairs in sum of reciprocals
David Eppstein
1/2/01
Read Re: Integer pairs in sum of reciprocals
r.e.s.
1/2/01
Read Re: Integer pairs in sum of reciprocals
r.e.s.
1/5/01
Read Re: Integer pairs in sum of reciprocals
the_great_nathan@my-deja.com
1/5/01
Read Re: Integer pairs in sum of reciprocals
r.e.s.
1/5/01
Read Re: Integer pairs in sum of reciprocals
Randy Poe
1/6/01
Read Re: Integer pairs in sum of reciprocals
the_great_nathan@my-deja.com
1/6/01
Read Re: Integer pairs in sum of reciprocals
David C. Ullrich
1/9/01
Read Re: Integer pairs in sum of reciprocals
the_great_nathan@my-deja.com
1/9/01
Read Re: Integer pairs in sum of reciprocals
David C. Ullrich
1/11/01
Read Re: Integer pairs in sum of reciprocals
the_great_nathan@my-deja.com
1/12/01
Read Re: Integer pairs in sum of reciprocals
David C. Ullrich
1/13/01
Read Re: Integer pairs in sum of reciprocals
the_great_nathan@my-deja.com
1/13/01
Read Re: Integer pairs in sum of reciprocals
David C. Ullrich
1/18/01
Read Re: Integer pairs in sum of reciprocals
the_great_nathan@my-deja.com
1/18/01
Read Re: Integer pairs in sum of reciprocals
David C. Ullrich
1/22/01
Read Re: Integer pairs in sum of reciprocals
the_great_nathan@my-deja.com
1/4/01
Read Re: Integer pairs in sum of reciprocals
Brian Evans
1/4/01
Read Re: Integer pairs in sum of reciprocals
Jan Kristian Haugland
1/5/01
Read Re: Integer pairs in sum of reciprocals
the_great_nathan@my-deja.com
1/5/01
Read Re: Integer pairs in sum of reciprocals
Dave Seaman
1/5/01
Read Re: Integer pairs in sum of reciprocals
David Eppstein
1/5/01
Read Re: Integer pairs in sum of reciprocals
Jan Kristian Haugland
1/6/01
Read Re: Integer pairs in sum of reciprocals
Damiano Scapeccia
1/7/01
Read Re: Integer pairs in sum of reciprocals
Adam Stephanides

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