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Integers not of the form $2^n+p^α q^β$

Jun-Jia Zhao
대한수학회 (The Korean Mathematical Society)|2024.11|대한수학회보 (Bulletin of the KMS)|제61권 제6호|pp. 1631-1637|DOI 10.4134/BKMS.b230719

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참고문헌

키워드

Romanoff type problemcovering systemprime power set
주제분류수학

초록

Let $\mathbb{N}$ and $\mathcal{P}$ denote the set of nonnegative integers and the set of odd primes, respectively. In this paper, we prove that if $r$ is a positive integer with $(r,30)=1$, then there is a positive proportion of primes $p$ such that $p^r\neq2^n+q_1^{\alpha} q_2^{\beta}$ for any $n,\alpha,\beta\in\mathbb{N},q_1,q_2\in\mathcal{P}$. This generalizes a result of Chen.

Abstract

Let $\mathbb{N}$ and $\mathcal{P}$ denote the set of nonnegative integers and the set of odd primes, respectively. In this paper, we prove that if $r$ is a positive integer with $(r,30)=1$, then there is a positive proportion of primes $p$ such that $p^r\neq2^n+q_1^{\alpha} q_2^{\beta}$ for any $n,\alpha,\beta\in\mathbb{N},q_1,q_2\in\mathcal{P}$. This generalizes a result of Chen.

참고문헌 (25)

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