Waring's problem in the natural numbers with binary expansions of a special type

TL;DR

This paper addresses Waring's problem within a special subset of natural numbers characterized by binary expansions with an even number of ones, providing a solution for this specific class.

Contribution

It extends Waring's problem to natural numbers with binary expansions of a particular type, a novel class not previously analyzed.

Findings

Waring's problem is solved for numbers with even binary ones.

The paper characterizes the representation of such numbers as sums of powers.

New methods are introduced for analyzing binary expansion properties.

Abstract

Let $\mathbb{N}_0$ be a class of natural numbers whose binary expansions contain even numbers of ones. Waring problem in numbers of class $\mathbb{N}_0$ is solved.