{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,20]],"date-time":"2026-04-20T23:38:53Z","timestamp":1776728333697,"version":"3.51.2"},"reference-count":15,"publisher":"American Mathematical Society (AMS)","issue":"239","license":[{"start":{"date-parts":[[2002,9,17]],"date-time":"2002-09-17T00:00:00Z","timestamp":1032220800000},"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                    A constructive version of a theorem of Thue is used to provide representations of certain integers as\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"x squared minus upper D y squared\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:msup>\n                              <mml:mi>x<\/mml:mi>\n                              <mml:mn>2<\/mml:mn>\n                            <\/mml:msup>\n                            <mml:mo>\n                              \u2212\n                              \n                            <\/mml:mo>\n                            <mml:mi>D<\/mml:mi>\n                            <mml:msup>\n                              <mml:mi>y<\/mml:mi>\n                              <mml:mn>2<\/mml:mn>\n                            <\/mml:msup>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">x^2-Dy^2<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    , where\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper D equals 2 comma 3 comma 5 comma 6 comma 7\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>D<\/mml:mi>\n                            <mml:mo>=<\/mml:mo>\n                            <mml:mn>2<\/mml:mn>\n                            <mml:mo>,<\/mml:mo>\n                            <mml:mn>3<\/mml:mn>\n                            <mml:mo>,<\/mml:mo>\n                            <mml:mn>5<\/mml:mn>\n                            <mml:mo>,<\/mml:mo>\n                            <mml:mn>6<\/mml:mn>\n                            <mml:mo>,<\/mml:mo>\n                            <mml:mn>7<\/mml:mn>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">D=2,3,5,6,7<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    .\n                  <\/p>","DOI":"10.1090\/s0025-5718-01-01381-3","type":"journal-article","created":{"date-parts":[[2002,9,20]],"date-time":"2002-09-20T15:46:54Z","timestamp":1032536814000},"page":"1281-1286","source":"Crossref","is-referenced-by-count":2,"title":["Thue\u2019s theorem and the diophantine equation \ud835\udc65\u00b2-\ud835\udc37\ud835\udc66\u00b2=\u00b1\ud835\udc41"],"prefix":"10.1090","volume":"71","author":[{"given":"Keith","family":"Matthews","sequence":"first","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2001,9,17]]},"reference":[{"key":"1","doi-asserted-by":"publisher","first-page":"1011","DOI":"10.2307\/2005889","article-title":"Note on representing a prime as a sum of two squares","volume":"26","author":"Brillhart, John","year":"1972","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"key":"2","unstructured":"G. Cornacchia, Su di un metodo per la risoluzione in numeri interi dell\u2019 equazione \u2211_{\u210e=0}\u207f\ud835\udc36_{\u210e}\ud835\udc65^{\ud835\udc5b-\u210e}=\ud835\udc43, Giornale di Matematiche di Battaglini 46 (1908) 33\u201390."},{"issue":"191","key":"3","doi-asserted-by":"publisher","first-page":"327","DOI":"10.2307\/2008809","article-title":"A deterministic algorithm for solving \ud835\udc5b=\ud835\udc53\ud835\udc62\u00b2+\ud835\udc54\ud835\udc63\u00b2 in coprime integers \ud835\udc62 and \ud835\udc63","volume":"55","author":"Hardy, Kenneth","year":"1990","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"key":"4","first-page":"225","article-title":"Solving \ud835\udc5b=\ud835\udc4e\ud835\udc62\u00b2+\ud835\udc4f\ud835\udc62\ud835\udc63+\ud835\udc50\ud835\udc63\u00b2 using the Euclidean algorithm","volume":"38","author":"Hardy, Kenneth","year":"1990","journal-title":"Utilitas Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0315-3681","issn-type":"print"},{"key":"5","unstructured":"C. Hermite, Note au sujet de l\u2019article pr\u00e9cedent, J. Math. Pures Appl., 13 (1848) 15."},{"key":"6","first-page":"109","article-title":"A refinement of the Hardy-Muskat-Williams algorithm for solving \ud835\udc5b=\ud835\udc53\ud835\udc62\u00b2+\ud835\udc54\ud835\udc63\u00b2","volume":"41","author":"Muskat, Joseph B.","year":"1992","journal-title":"Utilitas Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0315-3681","issn-type":"print"},{"key":"7","volume-title":"Introduction to number theory","author":"Nagell, Trygve","year":"1964","edition":"2"},{"issue":"4","key":"8","first-page":"358","article-title":"L\u2019algorithme de Cornacchia","volume":"13","author":"Nitaj, Abderrahmane","year":"1995","journal-title":"Exposition. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0723-0869","issn-type":"print"},{"key":"9","unstructured":"J.A. Serret, Sur un th\u00e9or\u00e8me r\u00e9latif aux nombres enti\u00e8res, J. Math. Pures Appl. 13 (1848) 12\u201314."},{"key":"10","isbn-type":"print","volume-title":"Selected mathematical papers","author":"Thue, Axel","year":"1977","ISBN":"https:\/\/id.crossref.org\/isbn\/8200016498"},{"key":"11","doi-asserted-by":"publisher","first-page":"531","DOI":"10.1090\/gsm\/058","article-title":"The 7-15 problem","volume":"9","author":"Venkatarayudu, T.","year":"1939","journal-title":"Proc. Indian Acad. Sci., Sect. A."},{"issue":"2","key":"12","doi-asserted-by":"publisher","first-page":"125","DOI":"10.2307\/2323912","article-title":"Editor\u2019s corner: the Euclidean algorithm strikes again","volume":"97","author":"Wagon, Stan","year":"1990","journal-title":"Amer. Math. Monthly","ISSN":"https:\/\/id.crossref.org\/issn\/0002-9890","issn-type":"print"},{"issue":"152","key":"13","doi-asserted-by":"publisher","first-page":"1347","DOI":"10.2307\/2006400","article-title":"An efficient algorithmic solution of the Diophantine equation \ud835\udc62\u00b2+5\ud835\udc63\u00b2=\ud835\udc5a","volume":"35","author":"Wilker, Peter","year":"1980","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"key":"14","first-page":"3","article-title":"On finding the solutions of \ud835\udc5b=\ud835\udc4e\ud835\udc62\u00b2+\ud835\udc4f\ud835\udc62\ud835\udc63+\ud835\udc50\ud835\udc63\u00b2 in integers \ud835\udc62 and \ud835\udc63","volume":"46","author":"Williams, Kenneth S.","year":"1994","journal-title":"Utilitas Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0315-3681","issn-type":"print"},{"key":"15","isbn-type":"print","first-page":"409","article-title":"Some refinements of an algorithm of Brillhart","author":"Williams, Kenneth S.","year":"1995","ISBN":"https:\/\/id.crossref.org\/isbn\/0821803123"}],"container-title":["Mathematics of Computation"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.ams.org\/mcom\/2002-71-239\/S0025-5718-01-01381-3\/S0025-5718-01-01381-3.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/www.ams.org\/mcom\/2002-71-239\/S0025-5718-01-01381-3\/S0025-5718-01-01381-3.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,20]],"date-time":"2026-04-20T23:00:50Z","timestamp":1776726050000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ams.org\/mcom\/2002-71-239\/S0025-5718-01-01381-3\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2001,9,17]]},"references-count":15,"journal-issue":{"issue":"239","published-print":{"date-parts":[[2002,7]]}},"alternative-id":["S0025-5718-01-01381-3"],"URL":"https:\/\/doi.org\/10.1090\/s0025-5718-01-01381-3","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":[[2001,9,17]]}}}