Every multiple of 4 except 212, 364, 420, and 428 is the sum of seven cubes

2009/03/26 by Kent D. Boklan, Noam D. Elkies, Boklan, Kent D. +1
Engineering · Mathematics · #11P05 #Analytic Number Theory Research #FOS: Mathematics #Limits and Structures in Graph Theory #Number Theory (math.NT) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.0903.4503

openalex publication_date 2009/03/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

It is conjectured that every integer N>454 is the sum of seven nonnegative cubes. We prove the conjecture when N is a multiple of 4.

Citations

• Quaternary Quadratic Forms Representing all Integers
• Waring's Problem

Related

• Every even number greater than 454 is the sum of seven cubes
• On Waring's Problem: Two Cubes and Two Minicubes
• On the representation of an even perfect number as the sum of a limited number of cubes
• Expressing an integer as a sum of cubes of polynomials
• Problems related to Waring-Goldbach problem involving cubes of primes