Breeding amicable numbers in abundance. II
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- by Stefan Battiato and Walter Borho PDF
- Math. Comp. 70 (2001), 1329-1333 Request permission
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.References
- Battiato, S.: Über die Produktion von 37803 neuen befreundeten Zahlenpaaren mit der Brütermethode, Diplom–Arbeit Wuppertal 1988 (unpublished).
- W. Borho and H. Hoffmann, Breeding amicable numbers in abundance, Math. Comp. 46 (1986), no. 173, 281–293. MR 815849, DOI 10.1090/S0025-5718-1986-0815849-1
- te Riele, H. et.al: Table of amicable pairs between $10^{10}$ and $10^{52}$, Centrum voor Wiskunde en Informatica, Note NM-N8GO3, Sept. 1986.
- S. Battiato and W. Borho, Are there odd amicable numbers not divisible by three?, Math. Comp. 50 (1988), no. 182, 633–637. MR 929559, DOI 10.1090/S0025-5718-1988-0929559-5
- Elvin J. Lee, Amicable numbers and the bilinear diophantine equation, Math. Comp. 22 (1968), 181–187. MR 224543, DOI 10.1090/S0025-5718-1968-0224543-9
Additional Information
- Stefan Battiato
- Affiliation: Sudermannstr. 2a, 40721 Hilden, Germany
- Walter Borho
- Affiliation: BUGH FB7, Gaußstraße 20, 42097 Wuppertal, Germany
- Received by editor(s): August 25, 1999
- Published electronically: October 17, 2000
- © Copyright 2000 American Mathematical Society
- Journal: Math. Comp. 70 (2001), 1329-1333
- MSC (2000): Primary 11A25
- DOI: https://doi.org/10.1090/S0025-5718-00-01279-5
- MathSciNet review: 1826584