Representation by sums of unlike powers

TL;DR

This paper proves that all sufficiently large integers can be expressed as a sum of thirteen positive integer powers with exponents from 2 to 14, improving the previous record of fourteen variables.

Contribution

It establishes a new minimal number of variables needed for representing large integers as sums of unlike powers, reducing the previous record from 14 to 13.

Findings

All sufficiently large integers can be represented with 13 variables.

The representation involves powers from 2 to 14.

The result improves the existing bounds in additive number theory.

Abstract

It is proved that all sufficiently large integers $n$ can be represented as $$n=x_1^2+x_2^3+\cdots+x_{13}^{14},$$ where $x_1,\ldots,x_{13}$ are positive integers. This improves upon the current record with $14$ variables in place of $13$.