A Diophantine Problem with Unlike Powers of Primes
Let k be an integer with 4≤k≤6 and η be any real number. Suppose that λ1,λ2,…,λ5 are nonzero real numbers, not all of them have the same sign, and λ1/λ2 is irrational. It is proved that the inequality λ1p1+λ2p22+λ3p33+λ4p44+λ5p5k+η<max1≤j≤5pj−σk has infinitely many solutions in prime variables p1...
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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/10.1155/2021/5528753 |
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| _version_ | 1850230957561348096 |
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| author | Quanwu Mu Liyan Xi |
| author_facet | Quanwu Mu Liyan Xi |
| author_sort | Quanwu Mu |
| collection | DOAJ |
| description | Let k be an integer with 4≤k≤6 and η be any real number. Suppose that λ1,λ2,…,λ5 are nonzero real numbers, not all of them have the same sign, and λ1/λ2 is irrational. It is proved that the inequality λ1p1+λ2p22+λ3p33+λ4p44+λ5p5k+η<max1≤j≤5pj−σk has infinitely many solutions in prime variables p1,p2,p3,p4, and p5, where 0<σ4<1/36,0<σ5<4/189, and 0<σ6<1/54. This gives an improvement of the recent results. |
| format | Article |
| id | doaj-art-06416718d1bb4cc4b3cc19e43dce5d56 |
| institution | OA Journals |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-06416718d1bb4cc4b3cc19e43dce5d562025-08-20T02:03:42ZengWileyJournal of Mathematics2314-46292314-47852021-01-01202110.1155/2021/55287535528753A Diophantine Problem with Unlike Powers of PrimesQuanwu Mu0Liyan Xi1School of Science, Xi’an Polytechnic University, Xi’an, 710048, Shaanxi, ChinaSchool of Science, Xi’an Polytechnic University, Xi’an, 710048, Shaanxi, ChinaLet k be an integer with 4≤k≤6 and η be any real number. Suppose that λ1,λ2,…,λ5 are nonzero real numbers, not all of them have the same sign, and λ1/λ2 is irrational. It is proved that the inequality λ1p1+λ2p22+λ3p33+λ4p44+λ5p5k+η<max1≤j≤5pj−σk has infinitely many solutions in prime variables p1,p2,p3,p4, and p5, where 0<σ4<1/36,0<σ5<4/189, and 0<σ6<1/54. This gives an improvement of the recent results.http://dx.doi.org/10.1155/2021/5528753 |
| spellingShingle | Quanwu Mu Liyan Xi A Diophantine Problem with Unlike Powers of Primes Journal of Mathematics |
| title | A Diophantine Problem with Unlike Powers of Primes |
| title_full | A Diophantine Problem with Unlike Powers of Primes |
| title_fullStr | A Diophantine Problem with Unlike Powers of Primes |
| title_full_unstemmed | A Diophantine Problem with Unlike Powers of Primes |
| title_short | A Diophantine Problem with Unlike Powers of Primes |
| title_sort | diophantine problem with unlike powers of primes |
| url | http://dx.doi.org/10.1155/2021/5528753 |
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