On squares of sums of three cubes

TL;DR

This paper demonstrates that nearly all positive integers can be expressed as the sum of four squares, where each square is itself a sum of three positive cubes, advancing understanding of representations of integers.

Contribution

It introduces a novel approach linking sums of three positive cubes to sums of squares, expanding the class of integers known to have such representations.

Findings

Almost every positive integer can be expressed as a sum of four squares of integers, each being a sum of three positive cubes.

The method establishes a new connection between sums of three cubes and sums of squares.

The result broadens the scope of integer representations in additive number theory.

Abstract

We show that almost every positive integer can be expressed as a sum of four squares of integers represented as the sums of three positive cubes.