The integral part of a nonlinear form with a square, a cube and a biquadrate
In this paper, we show that if λ1,λ2,λ3{\lambda }_{1},{\lambda }_{2},{\lambda }_{3} are non-zero real numbers, and at least one of the numbers λ1,λ2,λ3{\lambda }_{1},{\lambda }_{2},{\lambda }_{3} is irrational, then the integer parts of λ1n12+λ2n23+λ3n34{\lambda }_{1}{n}_{1}^{2}+{\lambda }_{2}{n}_{2...
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| Format: | Article |
| Language: | English |
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De Gruyter
2020-11-01
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| Series: | Open Mathematics |
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| Online Access: | https://doi.org/10.1515/math-2020-0069 |
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doaj-f2d1ed98adf14892ba5e3b04085b3e4f2021-09-06T19:20:12ZengDe GruyterOpen Mathematics2391-54552020-11-011811272128010.1515/math-2020-0069math-2020-0069The integral part of a nonlinear form with a square, a cube and a biquadrateGe Wenxu0Li Weiping1Zhao Feng2School of Mathematics and Statistics, North China University of Water Resources and Electric Power, Zhengzhou, 450046, People’s Republic of ChinaSchool of Mathematics and Information Sciences, Henan University of Economics and Law, Zhengzhou, 450000, People’s Republic of ChinaSchool of Mathematics and Information Sciences, Henan University of Economics and Law, Zhengzhou, 450000, People’s Republic of ChinaIn this paper, we show that if λ1,λ2,λ3{\lambda }_{1},{\lambda }_{2},{\lambda }_{3} are non-zero real numbers, and at least one of the numbers λ1,λ2,λ3{\lambda }_{1},{\lambda }_{2},{\lambda }_{3} is irrational, then the integer parts of λ1n12+λ2n23+λ3n34{\lambda }_{1}{n}_{1}^{2}+{\lambda }_{2}{n}_{2}^{3}+{\lambda }_{3}{n}_{3}^{4} are prime infinitely often for integers n1,n2,n3{n}_{1},{n}_{2},{n}_{3}. This gives an improvement of an earlier result.https://doi.org/10.1515/math-2020-0069diophantine inequalitiesprimesdavenport-heilbronn method11p3211p5511j25 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Ge Wenxu Li Weiping Zhao Feng |
| spellingShingle |
Ge Wenxu Li Weiping Zhao Feng The integral part of a nonlinear form with a square, a cube and a biquadrate Open Mathematics diophantine inequalities primes davenport-heilbronn method 11p32 11p55 11j25 |
| author_facet |
Ge Wenxu Li Weiping Zhao Feng |
| author_sort |
Ge Wenxu |
| title |
The integral part of a nonlinear form with a square, a cube and a biquadrate |
| title_short |
The integral part of a nonlinear form with a square, a cube and a biquadrate |
| title_full |
The integral part of a nonlinear form with a square, a cube and a biquadrate |
| title_fullStr |
The integral part of a nonlinear form with a square, a cube and a biquadrate |
| title_full_unstemmed |
The integral part of a nonlinear form with a square, a cube and a biquadrate |
| title_sort |
integral part of a nonlinear form with a square, a cube and a biquadrate |
| publisher |
De Gruyter |
| series |
Open Mathematics |
| issn |
2391-5455 |
| publishDate |
2020-11-01 |
| description |
In this paper, we show that if λ1,λ2,λ3{\lambda }_{1},{\lambda }_{2},{\lambda }_{3} are non-zero real numbers, and at least one of the numbers λ1,λ2,λ3{\lambda }_{1},{\lambda }_{2},{\lambda }_{3} is irrational, then the integer parts of λ1n12+λ2n23+λ3n34{\lambda }_{1}{n}_{1}^{2}+{\lambda }_{2}{n}_{2}^{3}+{\lambda }_{3}{n}_{3}^{4} are prime infinitely often for integers n1,n2,n3{n}_{1},{n}_{2},{n}_{3}. This gives an improvement of an earlier result. |
| topic |
diophantine inequalities primes davenport-heilbronn method 11p32 11p55 11j25 |
| url |
https://doi.org/10.1515/math-2020-0069 |
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