
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@mydeja.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 AbuJamal

