The integer part of nonlinear forms with prime variables

Weiping Li; Guohua Chen; Weiping Li; Guohua Chen

doi:10.3934/math.2022067

AIMS Mathematics

2022, Volume 7, Issue 1: 1147-1154. doi: 10.3934/math.2022067

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The integer part of nonlinear forms with prime variables

Weiping Li ^{1
,
,},
Guohua Chen ²

1.
Department of Mathematics and Information Science, Henan University of Economics and Law, Zhengzhou 450046, China
2.
School of Mathematics and Statistics, North China University of Water Resources and Electric Power, Zhengzhou 450046, China

Received: 17 August 2021 Accepted: 28 September 2021 Published: 20 October 2021
MSC : 11D75, 11P55

In this paper, we discuss problems that integer part of nonlinear forms with prime variables represent primes infinitely. We prove that under suitable conditions there exist infinitely many primes $ p_j, p $ such that $ [\lambda_1p_1^2+\lambda_2p_2^2+\lambda_3p_3^k] = p $ and $ [\lambda_1p_1^3+\cdots+\lambda_4p_4^3+\lambda_5p_5^k] = p $ with $ k\geq 2 $ and $ k\geq 3 $ respectively, which improve the author's earlier results.
- prime variables,
- Diophantine approximation,
- Davenport-Heilbronn method
Citation: Weiping Li, Guohua Chen. The integer part of nonlinear forms with prime variables[J]. AIMS Mathematics, 2022, 7(1): 1147-1154. doi: 10.3934/math.2022067

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Abstract

In this paper, we discuss problems that integer part of nonlinear forms with prime variables represent primes infinitely. We prove that under suitable conditions there exist infinitely many primes $ p_j, p $ such that $ [\lambda_1p_1^2+\lambda_2p_2^2+\lambda_3p_3^k] = p $ and $ [\lambda_1p_1^3+\cdots+\lambda_4p_4^3+\lambda_5p_5^k] = p $ with $ k\geq 2 $ and $ k\geq 3 $ respectively, which improve the author's earlier results.

References

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