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On a problem of Romanoff type

Volume 205 / 2022

Yuchen Ding Acta Arithmetica 205 (2022), 53-62 MSC: Primary 11P32; Secondary 11A41, 11B13. DOI: 10.4064/aa220207-14-6 Published online: 28 July 2022

Abstract

Let $\mathcal P$ be the set of primes. We prove that there is a positive lower density set of natural numbers which can be represented by the form $$p+2^{m_1^2}+2^{m_2^2} \quad (p\in \mathcal P,\,m_1,m_2\in \mathbb N).$$ This solves a 2014 problem of Chen and Yang.

Authors

  • Yuchen DingSchool of Mathematical Science
    Yangzhou University
    Yangzhou 225002, People’s Republic of China
    e-mail

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