On Sums of Seven Cubes
Identifieur interne : 002685 ( Crin/Curation ); précédent : 002684; suivant : 002686On Sums of Seven Cubes
Auteurs : François Bertault ; Olivier Ramaré ; Paul ZimmermannSource :
- Mathematics of Computation ; 1999.
English descriptors
Abstract
We show that every integer between 1290741 and 3.375\,10^{12} is a sum of 5 non negative 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 non negative cubes.
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<author><name sortKey="Bertault, Francois" sort="Bertault, Francois" uniqKey="Bertault F" first="François" last="Bertault">François Bertault</name>
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<author><name sortKey="Ramare, Olivier" sort="Ramare, Olivier" uniqKey="Ramare O" first="Olivier" last="Ramaré">Olivier Ramaré</name>
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<author><name sortKey="Zimmermann, Paul" sort="Zimmermann, Paul" uniqKey="Zimmermann P" first="Paul" last="Zimmermann">Paul Zimmermann</name>
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<front><div type="abstract" xml:lang="en" wicri:score="341">We show that every integer between 1290741 and 3.375\,10^{12} is a sum of 5 non negative 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 non negative cubes.</div>
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<BibTex type="article"><ref>bertault99a</ref>
<crinnumber>99-R-193</crinnumber>
<category>1</category>
<equipe>POLKA</equipe>
<author><e>Bertault, François</e>
<e>Ramaré, Olivier</e>
<e>Zimmermann, Paul</e>
</author>
<title>On Sums of Seven Cubes</title>
<journal>Mathematics of Computation</journal>
<year>1999</year>
<volume>68</volume>
<number>227</number>
<pages>1303-1310</pages>
<month>Jul</month>
<keywords><e>waring's problem for cubes</e>
<e>computational number theory</e>
</keywords>
<abstract>We show that every integer between 1290741 and 3.375\,10^{12} is a sum of 5 non negative 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 non negative cubes.</abstract>
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