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

 Messages: [ Previous | Next ]
 Dave Seaman Posts: 2,446 Registered: 12/6/04
Re: Integer pairs in sum of reciprocals
Posted: Jan 5, 2001 10:05 AM

In article <934e8d\$b8p\$1@nnrp1.deja.com>,
George Cantor <the_great_nathan@my-deja.com> wrote:
>In article <3A54D18A.CD2180B9@studNOSPAM.hia.no>,
> Jan Kristian Haugland <jkhaug00@studNOSPAM.hia.no> wrote:

>> Surely you are joking???

>What makes you think he is joking?

>Given: 1/A + 1/B = 1/2001 (A & B are positive integers)

>First, the sum would be too large if either A or B
>were less than 2002. Second, the sum would be too
>small if both A and B were greater than 4002. So,
>one of the variables must be between 2002 and 4002,
>but an exhaustive search of that range, taking less
>than .00001 seconds, uncovers no solutions.

You wouldn't by any chance have used floating point arithmetic in
conducting the search, would you?

A quick search with Mathematica turns up 13 solutions. Note that a = b =
4002 is not a solution because of the requirement a < b, and therefore we
need only search to 4001.

In[1]= Select[Range[2002, 4001], IntegerQ[1/(1/2001 - 1/#)] &]

Out[1]= {2002, 2004, 2010, 2024, 2030, 2070, 2088, 2208, 2262, 2530,
2668, 2842, 3588}

--
Dave Seaman dseaman@purdue.edu
Amnesty International calls for new trial for Mumia Abu-Jamal