Abstract of: Amicable pairs, a survey

MAS-R0307
M. García ; J.M. Pedersen ; H.J.J. te Riele ;
2003, MAS-R0307, ISSN 1386-3703
PDF-file compressed PostScript ( 314 KB ) ( 17 pages )
 
Abstract
In 1750, Euler [20, 21] published an extensive paper on amicable pairs, by which he added fifty-nine new amicable pairs to the three amicable pairs known thus far. In 1972, Lee and Madachy [45] published a historical survey of amicable pairs, with a list of the 1108 amicable pairs then known. In 1995, Pedersen [48] started to create and maintain an Internet site with lists of all the known amicable pairs. The current (February 2003) number of amicable pairs in these lists exceeds four million. The purpose of this paper is to update the 1972 paper of Lee and Madachy, in order to document the developments which have led to the explosion of known amicable pairs in the past thirty years. We hope that this may stimulate research in the direction of finding a proof that the number of amicable pairs is infinite.

 
CWI Group(s):
MAS2 (Scientific Computing and Control Theory)
 
CWI Project(s):
Computational number theory
 
Keywords:
Amicable numbers