{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T11:02:46Z","timestamp":1776769366723,"version":"3.51.2"},"reference-count":5,"publisher":"American Mathematical Society (AMS)","issue":"235","license":[{"start":{"date-parts":[[2001,10,17]],"date-time":"2001-10-17T00:00:00Z","timestamp":1003276800000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>In a first article of this title, new procedures were described to compute many amicable numbers by \u201cbreeding\u201d 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\u00a0Riele 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.<\/p>","DOI":"10.1090\/s0025-5718-00-01279-5","type":"journal-article","created":{"date-parts":[[2002,11,6]],"date-time":"2002-11-06T14:02:22Z","timestamp":1036591342000},"page":"1329-1333","source":"Crossref","is-referenced-by-count":3,"title":["Breeding amicable numbers in abundance. II"],"prefix":"10.1090","volume":"70","author":[{"given":"Stefan","family":"Battiato","sequence":"first","affiliation":[]},{"given":"Walter","family":"Borho","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2000,10,17]]},"reference":[{"key":"1","unstructured":"Battiato, S.: \u00dcber die Produktion von 37803 neuen befreundeten Zahlenpaaren mit der Br\u00fctermethode, Diplom\u2013Arbeit Wuppertal 1988 (unpublished)."},{"issue":"173","key":"2","doi-asserted-by":"publisher","first-page":"281","DOI":"10.2307\/2008232","article-title":"Breeding amicable numbers in abundance","volume":"46","author":"Borho, W.","year":"1986","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"key":"3","unstructured":"te Riele, H. et.al: Table of amicable pairs between 10\u00b9\u2070 and 10\u2075\u00b2, Centrum voor Wiskunde en Informatica, Note NM-N8GO3, Sept. 1986."},{"issue":"182","key":"4","doi-asserted-by":"publisher","first-page":"633","DOI":"10.2307\/2008630","article-title":"Are there odd amicable numbers not divisible by three?","volume":"50","author":"Battiato, S.","year":"1988","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"key":"5","doi-asserted-by":"publisher","first-page":"181","DOI":"10.2307\/2004776","article-title":"Amicable numbers and the bilinear diophantine equation","volume":"22","author":"Lee, Elvin J.","year":"1968","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"}],"container-title":["Mathematics of Computation"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.ams.org\/mcom\/2001-70-235\/S0025-5718-00-01279-5\/S0025-5718-00-01279-5.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/www.ams.org\/mcom\/2001-70-235\/S0025-5718-00-01279-5\/S0025-5718-00-01279-5.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,20]],"date-time":"2026-04-20T22:42:21Z","timestamp":1776724941000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ams.org\/mcom\/2001-70-235\/S0025-5718-00-01279-5\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2000,10,17]]},"references-count":5,"journal-issue":{"issue":"235","published-print":{"date-parts":[[2001,7]]}},"alternative-id":["S0025-5718-00-01279-5"],"URL":"https:\/\/doi.org\/10.1090\/s0025-5718-00-01279-5","archive":["CLOCKSS","Portico"],"relation":{},"ISSN":["1088-6842","0025-5718"],"issn-type":[{"value":"1088-6842","type":"electronic"},{"value":"0025-5718","type":"print"}],"subject":[],"published":{"date-parts":[[2000,10,17]]}}}