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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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
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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| Summary: | 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. |
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| ISSN: | 2314-4629 2314-4785 |