On a problem of Romanoff type
Volume 205 / 2022
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.
