Generalization of Romanoff's theorem

TL;DR

This paper extends Romanoff's theorem and explores related sums involving Euler's totient function, providing new insights into number theory and additive properties of special number sets.

Contribution

It introduces a generalized version of Romanoff's theorem and presents new results on sums connected to Euler's totient function.

Findings

Generalization of Romanoff's theorem achieved

New bounds or identities for sums involving Euler's totient function

Enhanced understanding of additive number theory properties

Abstract

We generalize Romanoff's theorem. Also, we obtain a result on sums related to Euler's totient function.