A. Radomskii

A Romanoff-type theorem for a multiset of products of powers

Let $b_1,\dots,b_d\ge2$ be fixed integers, and let $k$ be their multiplicative rank. We study representations $n=a+b_1^{u_1}\cdots b_d^{u_d}$, where $a$ belongs to a set $\mathcal{A}$ of positive integers and $u_1,\dots,u_d$ are positive integers, counting distinct tuples of exponents separately. Under density and corr...