{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,18]],"date-time":"2026-03-18T07:49:34Z","timestamp":1773820174265,"version":"3.50.1"},"reference-count":15,"publisher":"American Mathematical Society (AMS)","issue":"227","license":[{"start":{"date-parts":[[2000,2,11]],"date-time":"2000-02-11T00:00:00Z","timestamp":950227200000},"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>We show that every integer between 1290741 and <inline-formula content-type=\"math\/mathml\">\n<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"3.375 times 10 Superscript 12\">\n  <mml:semantics>\n    <mml:mrow>\n      <mml:mn>3.375<\/mml:mn>\n      <mml:mo>\u00d7<\/mml:mo>\n      <mml:msup>\n        <mml:mn>10<\/mml:mn>\n        <mml:mrow class=\"MJX-TeXAtom-ORD\">\n          <mml:mn>12<\/mml:mn>\n        <\/mml:mrow>\n      <\/mml:msup>\n    <\/mml:mrow>\n    <mml:annotation encoding=\"application\/x-tex\">3.375\\times 10^{12}<\/mml:annotation>\n  <\/mml:semantics>\n<\/mml:math>\n<\/inline-formula> is a sum of 5 nonnegative cubes, from which we deduce that every integer which is a cubic residue modulo 9 and an invertible cubic residue modulo 37 is a sum of 7 nonnegative cubes.<\/p>","DOI":"10.1090\/s0025-5718-99-01071-6","type":"journal-article","created":{"date-parts":[[2002,7,26]],"date-time":"2002-07-26T22:13:45Z","timestamp":1027721625000},"page":"1303-1310","source":"Crossref","is-referenced-by-count":5,"title":["On sums of seven cubes"],"prefix":"10.1090","volume":"68","author":[{"given":"F.","family":"Bertault","sequence":"first","affiliation":[]},{"given":"O.","family":"Ramar\u00e9","sequence":"additional","affiliation":[]},{"given":"P.","family":"Zimmermann","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[1999,2,11]]},"reference":[{"key":"1","doi-asserted-by":"crossref","unstructured":"W.S. Baer \u201c\u00dcber die Zerlegung der ganzen Zahlen in sieben Kuben\u201d, Math. Ann. (1913) Vol 74, pp 511-515.","DOI":"10.1007\/BF01456910"},{"issue":"1","key":"2","doi-asserted-by":"publisher","first-page":"118","DOI":"10.1007\/BF01934077","article-title":"Numerical investigation of Waring\u2019s problem for cubes","volume":"21","author":"Bohman, Jan","year":"1981","journal-title":"BIT","ISSN":"https:\/\/id.crossref.org\/issn\/0006-3835","issn-type":"print"},{"key":"3","unstructured":"J.M. Deshouillers, F. Hennecart and B. Landreau, private communication."},{"key":"4","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."},{"key":"5","unstructured":"L. E. Dickson \u201cTheory of numbers\u201d, Vol II, Chelsea Publishing Company (1971)."},{"key":"6","doi-asserted-by":"crossref","unstructured":"G. H. Hardy and J.E. Littlewood \u201cSome problems of \u201cPartitio Numerorum\u201d IV. The singular series in Waring\u2019s Problem and the value of the number \ud835\udc3a(\ud835\udc58)\u201d, Math. Zeitschrift (1922) Vol 12, pp 161\u2013188.","DOI":"10.1007\/BF01482074"},{"key":"7","doi-asserted-by":"crossref","unstructured":"A. J. Kempner \u201c\u00dcber das Waringsche Problem und einige Verallgemeinerungen\u201d Diss. G\u00f6ttingen, 1912. Extract in Math. Annalen, (1912), Vol 72, pp 387.","DOI":"10.1007\/BF01456723"},{"issue":"1","key":"8","first-page":"1","article-title":"\u00c9tude probabiliste des sommes de \ud835\udc60 puissances \ud835\udc60-i\u00e8mes","volume":"99","author":"Landreau, Bernard","year":"1995","journal-title":"Compositio Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0010-437X","issn-type":"print"},{"issue":"2","key":"9","doi-asserted-by":"publisher","first-page":"176","DOI":"10.1016\/0022-314X(84)90100-8","article-title":"An effective seven cube theorem","volume":"19","author":"McCurley, Kevin S.","year":"1984","journal-title":"J. Number Theory","ISSN":"https:\/\/id.crossref.org\/issn\/0022-314X","issn-type":"print"},{"issue":"213","key":"10","doi-asserted-by":"publisher","first-page":"397","DOI":"10.1090\/S0025-5718-96-00669-2","article-title":"Primes in arithmetic progressions","volume":"65","author":"Ramar\u00e9, Olivier","year":"1996","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"issue":"4","key":"11","doi-asserted-by":"publisher","first-page":"415","DOI":"10.1007\/BF02575769","article-title":"Computations concerning Waring\u2019s problem for cubes","volume":"19","author":"Romani, F.","year":"1982","journal-title":"Calcolo","ISSN":"https:\/\/id.crossref.org\/issn\/0008-0624","issn-type":"print"},{"key":"12","doi-asserted-by":"publisher","first-page":"122","DOI":"10.1515\/crll.1986.365.122","article-title":"On Waring\u2019s problem for cubes","volume":"365","author":"Vaughan, R. C.","year":"1986","journal-title":"J. Reine Angew. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0075-4102","issn-type":"print"},{"issue":"1-2","key":"13","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/BF02392834","article-title":"A new iterative method in Waring\u2019s problem","volume":"162","author":"Vaughan, R. C.","year":"1989","journal-title":"Acta Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0001-5962","issn-type":"print"},{"issue":"2","key":"14","doi-asserted-by":"publisher","first-page":"205","DOI":"10.1112\/jlms\/s2-39.2.205","article-title":"On Waring\u2019s problem for cubes. II","volume":"39","author":"Vaughan, R. C.","year":"1989","journal-title":"J. London Math. Soc. (2)","ISSN":"https:\/\/id.crossref.org\/issn\/0024-6107","issn-type":"print"},{"key":"15","first-page":"623","article-title":"Annihilator ideals and representation iteration for abstract rings","volume":"5","author":"Everett, C. J., Jr.","year":"1939","journal-title":"Duke Math. J.","ISSN":"https:\/\/id.crossref.org\/issn\/0012-7094","issn-type":"print"}],"container-title":["Mathematics of Computation"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.ams.org\/mcom\/1999-68-227\/S0025-5718-99-01071-6\/S0025-5718-99-01071-6.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/www.ams.org\/mcom\/1999-68-227\/S0025-5718-99-01071-6\/S0025-5718-99-01071-6.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,11,3]],"date-time":"2021-11-03T00:07:30Z","timestamp":1635898050000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ams.org\/mcom\/1999-68-227\/S0025-5718-99-01071-6\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1999,2,11]]},"references-count":15,"journal-issue":{"issue":"227","published-print":{"date-parts":[[1999,7]]}},"alternative-id":["S0025-5718-99-01071-6"],"URL":"https:\/\/doi.org\/10.1090\/s0025-5718-99-01071-6","archive":["CLOCKSS","Portico"],"relation":{},"ISSN":["0025-5718","1088-6842"],"issn-type":[{"value":"0025-5718","type":"print"},{"value":"1088-6842","type":"electronic"}],"subject":[],"published":{"date-parts":[[1999,2,11]]}}}