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<p>This article aims to investigate whether there exist infinitely many primes <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$ p $</EquationSource> </InlineEquation>such that <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$ \lfloor\alpha_{1}p^{c_{1}}+\alpha_{2}p^{c_{2}}+\beta\rfloor $</EquationSource> </InlineEquation> is also a primefor almost all irrationals <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$ \alpha_{1}&gt;0 $</EquationSource> </InlineEquation> and <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$ \alpha_{2}&gt;0 $</EquationSource> </InlineEquation> (in the sense of Lebesgue measure).Our result provides an affirmative answer to this question by utilizing elementary and analytic methods,especially the division trick and estimates of exponential sums.</p>

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On Primes of the Form \( \lfloor\alpha_{1}p^{c_{1}}+\alpha_{2}p^{c_{2}}+\beta\rfloor \)

  • 期刊论文

  • 发表日期：

    2026年3月28日

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  • Y. Song

摘要

This article aims to investigate whether there exist infinitely many primes $ p $ such that $ \lfloor\alpha_{1}p^{c_{1}}+\alpha_{2}p^{c_{2}}+\beta\rfloor $ is also a primefor almost all irrationals $ \alpha_{1}>0 $ and $ \alpha_{2}>0 $ (in the sense of Lebesgue measure).Our result provides an affirmative answer to this question by utilizing elementary and analytic methods,especially the division trick and estimates of exponential sums.