On a Diophantine problem with two primes and s powers of two

Abstract

We refine a recent result of Parsell on the values of the form ${\lambda }_1{p}_1+{\lambda }_2{p}_2+{\mu }_1{2}^{m_1}+...m+{\mu }_s{2}^{m_s},$ where $p_1,p_2$ are prime numbers, $m_1,...c,m_s$ are positive integers, ${\lambda }_1/{\lambda }_2$ is negative and irrational and ${\lambda }_1/{\mu }_1$, $λ_2/μ_2 \in \Q$.

arXiv commentv2: enlarged introduction, improved major arc estimate