{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T19:36:18Z","timestamp":1776800178683,"version":"3.51.2"},"reference-count":23,"publisher":"American Mathematical Society (AMS)","issue":"298","license":[{"start":{"date-parts":[[2016,7,16]],"date-time":"2016-07-16T00:00:00Z","timestamp":1468627200000},"content-version":"am","delay-in-days":366,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>\n                    We propose a conjecture, similar to Skolem\u2019s conjecture, on a Hasse-type principle for exponential Diophantine equations. We prove that in a sense the principle is valid for \u201calmost all\u201d equations. Based upon this we propose a general method for the solution of exponential Diophantine equations. Using a generalization of a result of Erd\u0151s, Pomerance and Schmutz concerning Carmichael\u2019s\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"lamda\">\n                        <mml:semantics>\n                          <mml:mi>\n                            \u03bb\n                            \n                          <\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">\\lambda<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    function, we can make our search systematic for certain moduli needed in the method.\n                  <\/p>","DOI":"10.1090\/mcom\/3002","type":"journal-article","created":{"date-parts":[[2015,7,16]],"date-time":"2015-07-16T08:50:32Z","timestamp":1437036632000},"page":"849-860","source":"Crossref","is-referenced-by-count":16,"title":["A Hasse-type principle for exponential Diophantine equations and its applications"],"prefix":"10.1090","volume":"85","author":[{"given":"Csan\u00e1d","family":"Bert\u00f3k","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lajos","family":"Hajdu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"14","published-online":{"date-parts":[[2015,7,16]]},"reference":[{"issue":"2","key":"1","doi-asserted-by":"publisher","first-page":"101","DOI":"10.4064\/aa138-2-1","article-title":"Representing integers as linear combinations of \ud835\udc46-units","volume":"138","author":"\u00c1d\u00e1m, Zs.","year":"2009","journal-title":"Acta Arith.","ISSN":"https:\/\/id.crossref.org\/issn\/0065-1036","issn-type":"print"},{"issue":"1","key":"2","doi-asserted-by":"publisher","first-page":"11","DOI":"10.1216\/rmjm\/1181072793","article-title":"On the Diophantine equation 1+\ud835\udc65+\ud835\udc66=\ud835\udc67","volume":"22","author":"Alex, Leo J.","year":"1992","journal-title":"Rocky Mountain J. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0035-7596","issn-type":"print"},{"issue":"1","key":"3","first-page":"13","article-title":"On the Diophantine equation \ud835\udc64+\ud835\udc65+\ud835\udc66=\ud835\udc67, with \ud835\udc64\ud835\udc65\ud835\udc66\ud835\udc67=2^{\ud835\udc5f}3^{\ud835\udc60}5^{\ud835\udc61}","volume":"8","author":"Alex, L. J.","year":"1995","journal-title":"Rev. Mat. Univ. Complut. Madrid","ISSN":"https:\/\/id.crossref.org\/issn\/0214-3577","issn-type":"print"},{"issue":"3","key":"4","doi-asserted-by":"publisher","first-page":"407","DOI":"10.1215\/00127094-2009-056","article-title":"Small points on subvarieties of a torus","volume":"150","author":"Amoroso, Francesco","year":"2009","journal-title":"Duke Math. 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Skolem, Anwendung exponentieller Kongruenzen zum Beweis der Unlsbarkeit gewisser diophantischer Gleichungen, Vid. akad. Avh. Oslo I 1937 nr 12."},{"key":"21","unstructured":"W. A. Stein et al., Sage Mathematics Software (Version 6.1.1), The Sage Development Team, 2014, http:\/\/www.sagemath.org."},{"issue":"21-24","key":"22","doi-asserted-by":"publisher","first-page":"1135","DOI":"10.1049\/iet-ipr.2010.0499","article-title":"On the exponential Diophantine equation (4\ud835\udc5a\u00b2+1)^{\ud835\udc65}+(5\ud835\udc5a\u00b2-1)^{\ud835\udc66}=(3\ud835\udc5a)^{\ud835\udc67}","volume":"6","author":"Terai, Nobuhiro","year":"2012","journal-title":"Int. J. 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