{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T08:42:18Z","timestamp":1776847338306,"version":"3.51.2"},"reference-count":14,"publisher":"American Mathematical Society (AMS)","issue":"268","license":[{"start":{"date-parts":[[2010,2,13]],"date-time":"2010-02-13T00:00:00Z","timestamp":1266019200000},"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>\n                    In relation to Hall\u2019s conjecture, a new algorithm is presented to search for small nonzero\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"k equals StartAbsoluteValue x cubed minus y squared EndAbsoluteValue\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>k<\/mml:mi>\n                            <mml:mo>=<\/mml:mo>\n                            <mml:mo fence=\"false\" stretchy=\"false\">\n                              |\n                              \n                            <\/mml:mo>\n                            <mml:msup>\n                              <mml:mi>x<\/mml:mi>\n                              <mml:mn>3<\/mml:mn>\n                            <\/mml:msup>\n                            <mml:mo>\n                              \u2212\n                              \n                            <\/mml:mo>\n                            <mml:msup>\n                              <mml:mi>y<\/mml:mi>\n                              <mml:mn>2<\/mml:mn>\n                            <\/mml:msup>\n                            <mml:mo fence=\"false\" stretchy=\"false\">\n                              |\n                              \n                            <\/mml:mo>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">k=\\lvert x^3-y^2\\rvert<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    values. Seventeen new values of\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"k greater-than x Superscript 1 slash 2\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>k<\/mml:mi>\n                            <mml:mo>&gt;<\/mml:mo>\n                            <mml:msup>\n                              <mml:mi>x<\/mml:mi>\n                              <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                                <mml:mn>1<\/mml:mn>\n                                <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                                  <mml:mo>\/<\/mml:mo>\n                                <\/mml:mrow>\n                                <mml:mn>2<\/mml:mn>\n                              <\/mml:mrow>\n                            <\/mml:msup>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">k&gt;x^{1\/2}<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    are reported.\n                  <\/p>","DOI":"10.1090\/s0025-5718-09-02240-6","type":"journal-article","created":{"date-parts":[[2009,6,30]],"date-time":"2009-06-30T10:39:02Z","timestamp":1246358342000},"page":"2435-2444","source":"Crossref","is-referenced-by-count":2,"title":["A new algorithm to search for small nonzero |\ud835\udc65\u00b3-\ud835\udc66\u00b2| values"],"prefix":"10.1090","volume":"78","author":[{"given":"I.","family":"Calvo","sequence":"first","affiliation":[]},{"given":"J.","family":"Herranz","sequence":"additional","affiliation":[]},{"given":"G.","family":"S\u00e1ez","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2009,2,13]]},"reference":[{"key":"1","doi-asserted-by":"publisher","first-page":"173","DOI":"10.1098\/rsta.1968.0010","article-title":"Contributions to the theory of Diophantine equations. 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