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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Breeding amicable numbers in abundance. II


Authors: Stefan Battiato and Walter Borho
Journal: Math. Comp. 70 (2001), 1329-1333
MSC (2000): Primary 11A25
Published electronically: October 17, 2000
MathSciNet review: 1826584
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Abstract: In a first article of this title, new procedures were described to compute many amicable numbers by ``breeding'' them in several generations. An extensive computer search was later performed (in 1988), and demonstrated the remarkable effectiveness of this breeding method: the number of known amicable pairs was easily quadrupled by this search. As we learnt recently (1999) from the internet, Pederson and te Riele have again multiplied that number roughly by ten. While they give no information on their method of search, we publish here our method and summarize the computations. Our results provide some evidence for the conjecture that the number of amicable pairs is infinite.


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Additional Information

Stefan Battiato
Affiliation: Sudermannstr. 2a, 40721 Hilden, Germany

Walter Borho
Affiliation: BUGH FB7, Gaußstraße 20, 42097 Wuppertal, Germany

DOI: http://dx.doi.org/10.1090/S0025-5718-00-01279-5
PII: S 0025-5718(00)01279-5
Received by editor(s): August 25, 1999
Published electronically: October 17, 2000
Article copyright: © Copyright 2000 American Mathematical Society