Every even number greater than 454 is the sum of seven cubes

TL;DR

This paper proves that every even number greater than 454 can be expressed as the sum of seven cubes, confirming a longstanding conjecture for all such numbers.

Contribution

The authors prove the conjecture for even numbers congruent to 2 mod 4, completing the proof for all even integers greater than 454.

Findings

Confirmed the conjecture for N ≡ 2 mod 4

Combined with recent results for multiples of 4, proved the conjecture for all even N>454

Established the sum of seven cubes representation for all even numbers above 454

Abstract

It is conjectured that every integer N>454 is the sum of seven nonnegative cubes. We prove the conjecture when N is congruent to 2 mod 4. This result, together with a recent proof for 4|N, shows that the conjecture is true for all even N.