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

2010/09/21 by Noam D. Elkies, Elkies, Noam D.
Engineering · Mathematics · #Analytic Number Theory Research #FOS: Mathematics #Limits and Structures in Graph Theory #Number Theory (math.NT) #Primary 11P05 #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1009.3983

openalex publication_date 2010/09/21 · 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 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.

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