A System of Two Diophantine Inequalities with Primes
Let 1<d<c<128/119, 1<α<β<61−d/c. In this paper, we prove that there exist positive real numbers N10 and N20 depending on c,d,α,β such that for all real numbers N1>N10, N2>N20 and α≤N2/N1d/c≤β, the system of two Diophantine inequalities p1c+⋯+p6c−N1<N1−1/c128/119−clog109N1,...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/6613947 |
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| _version_ | 1832550874452328448 |
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| author | Xue Han Huafeng Liu Deyu Zhang |
| author_facet | Xue Han Huafeng Liu Deyu Zhang |
| author_sort | Xue Han |
| collection | DOAJ |
| description | Let 1<d<c<128/119, 1<α<β<61−d/c. In this paper, we prove that there exist positive real numbers N10 and N20 depending on c,d,α,β such that for all real numbers N1>N10, N2>N20 and α≤N2/N1d/c≤β, the system of two Diophantine inequalities p1c+⋯+p6c−N1<N1−1/c128/119−clog109N1,p1d+⋯+p6d−N2<N2−1/d128/119−dlog109N2 is solvable in prime variables p1,…,p6. |
| format | Article |
| id | doaj-art-ea1492ffcf52448882f425e2478ffd39 |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-ea1492ffcf52448882f425e2478ffd392025-02-03T06:05:45ZengWileyJournal of Mathematics2314-46292314-47852021-01-01202110.1155/2021/66139476613947A System of Two Diophantine Inequalities with PrimesXue Han0Huafeng Liu1Deyu Zhang2School of Mathematics and Statistics, Shandong Normal University, Jinan, Shandong 250358, ChinaSchool of Mathematics and Statistics, Shandong Normal University, Jinan, Shandong 250358, ChinaSchool of Mathematics and Statistics, Shandong Normal University, Jinan, Shandong 250358, ChinaLet 1<d<c<128/119, 1<α<β<61−d/c. In this paper, we prove that there exist positive real numbers N10 and N20 depending on c,d,α,β such that for all real numbers N1>N10, N2>N20 and α≤N2/N1d/c≤β, the system of two Diophantine inequalities p1c+⋯+p6c−N1<N1−1/c128/119−clog109N1,p1d+⋯+p6d−N2<N2−1/d128/119−dlog109N2 is solvable in prime variables p1,…,p6.http://dx.doi.org/10.1155/2021/6613947 |
| spellingShingle | Xue Han Huafeng Liu Deyu Zhang A System of Two Diophantine Inequalities with Primes Journal of Mathematics |
| title | A System of Two Diophantine Inequalities with Primes |
| title_full | A System of Two Diophantine Inequalities with Primes |
| title_fullStr | A System of Two Diophantine Inequalities with Primes |
| title_full_unstemmed | A System of Two Diophantine Inequalities with Primes |
| title_short | A System of Two Diophantine Inequalities with Primes |
| title_sort | system of two diophantine inequalities with primes |
| url | http://dx.doi.org/10.1155/2021/6613947 |
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