{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T20:44:14Z","timestamp":1776804254319,"version":"3.51.2"},"reference-count":8,"publisher":"American Mathematical Society (AMS)","issue":"314","license":[{"start":{"date-parts":[[2019,1,18]],"date-time":"2019-01-18T00:00:00Z","timestamp":1547769600000},"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":"

\n A good example of Hall\u2019s conjecture is a pair of natural numbers\n \n \n \n \n x<\/mml:mi>\n ,<\/mml:mo>\n y<\/mml:mi>\n <\/mml:mrow>\n x,y<\/mml:annotation>\n <\/mml:semantics>\n <\/mml:math>\n <\/inline-formula>\n such that\n \n \n \n \n 0<\/mml:mn>\n ><\/mml:mo>\n \n |<\/mml:mo>\n <\/mml:mrow>\n \n x<\/mml:mi>\n 3<\/mml:mn>\n <\/mml:msup>\n \n \u2212\n \n <\/mml:mo>\n \n y<\/mml:mi>\n 2<\/mml:mn>\n <\/mml:msup>\n \n |<\/mml:mo>\n <\/mml:mrow>\n ><\/mml:mo>\n \n x<\/mml:mi>\n \n 1<\/mml:mn>\n \n \/<\/mml:mo>\n <\/mml:mrow>\n 2<\/mml:mn>\n <\/mml:mrow>\n <\/mml:msup>\n <\/mml:mrow>\n 0 > |x^3 - y^2| > x^{1\/2}<\/mml:annotation>\n <\/mml:semantics>\n <\/mml:math>\n <\/inline-formula>\n . We have implemented a new algorithm and found nine not previously known good examples. Moreover, we have verified that all good examples with\n \n \n \n \n x<\/mml:mi>\n ><\/mml:mo>\n \n 10<\/mml:mn>\n \n 29<\/mml:mn>\n <\/mml:mrow>\n <\/mml:msup>\n <\/mml:mrow>\n x > 10^{29}<\/mml:annotation>\n <\/mml:semantics>\n <\/mml:math>\n <\/inline-formula>\n are now found.\n <\/p>","DOI":"10.1090\/mcom\/3298","type":"journal-article","created":{"date-parts":[[2017,8,30]],"date-time":"2017-08-30T10:04:25Z","timestamp":1504087465000},"page":"2903-2914","source":"Crossref","is-referenced-by-count":1,"title":["Search for good examples of Hall\u2019s conjecture"],"prefix":"10.1090","volume":"87","author":[{"given":"St\u00e5l","family":"Aanderaa","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lars","family":"Kristiansen","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hans Kristian","family":"Ruud","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"14","published-online":{"date-parts":[[2018,1,18]]},"reference":[{"issue":"268","key":"1","doi-asserted-by":"publisher","first-page":"2435","DOI":"10.1090\/S0025-5718-09-02240-6","article-title":"A new algorithm to search for small nonzero |\ud835\udc65\u00b3-\ud835\udc66\u00b2| values","volume":"78","author":"Jim\u00e9nez Calvo, I.","year":"2009","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"issue":"3","key":"2","first-page":"273","article-title":"The Diophantine equation \ud835\udc65\u00b3-\ud835\udc66\u00b2=\ud835\udc58 and a conjecture of M. Hall","volume":"32","author":"Danilov, L. V.","year":"1982","journal-title":"Mat. Zametki","ISSN":"https:\/\/id.crossref.org\/issn\/0025-567X","issn-type":"print"},{"key":"3","isbn-type":"print","doi-asserted-by":"publisher","first-page":"33","DOI":"10.1007\/10722028_2","article-title":"Rational points near curves and small nonzero |\ud835\udc65\u00b3-\ud835\udc66\u00b2| via lattice reduction","author":"Elkies, Noam D.","year":"2000","ISBN":"https:\/\/id.crossref.org\/isbn\/3540676953"},{"key":"4","first-page":"173","article-title":"The Diophantine equation \ud835\udc65\u00b3-\ud835\udc66\u00b2=\ud835\udc58","author":"Hall, Marshall, Jr.","year":"1971"},{"issue":"3","key":"5","doi-asserted-by":"publisher","first-page":"335","DOI":"10.1023\/A:1000281602647","article-title":"On Mordell\u2019s equation","volume":"110","author":"Gebel, J.","year":"1998","journal-title":"Compositio Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0010-437X","issn-type":"print"},{"key":"6","volume-title":"Continued fractions","author":"Khintchine, A. Ya.","year":"1963"},{"key":"7","isbn-type":"print","volume-title":"An introduction to the theory of numbers","author":"Niven, Ivan","year":"1991","ISBN":"https:\/\/id.crossref.org\/isbn\/0471625469","edition":"5"},{"key":"8","unstructured":"\\url{http:\/\/ijcalvo.galeon.com\/hall.htm}"}],"container-title":["Mathematics of Computation"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.ams.org\/mcom\/2018-87-314\/S0025-5718-2018-03298-7\/S0025-5718-2018-03298-7.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/www.ams.org\/mcom\/2018-87-314\/S0025-5718-2018-03298-7\/S0025-5718-2018-03298-7.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T19:49:33Z","timestamp":1776800973000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ams.org\/mcom\/2018-87-314\/S0025-5718-2018-03298-7\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,1,18]]},"references-count":8,"journal-issue":{"issue":"314","published-print":{"date-parts":[[2018,11]]}},"alternative-id":["S0025-5718-2018-03298-7"],"URL":"https:\/\/doi.org\/10.1090\/mcom\/3298","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":[[2018,1,18]]}}}