Every integer greater than 454 is the sum of at most seven positive cubes

DOI10.2140/ANT.2016.10.2093zbMath1407.11115arXiv1505.00647OpenAlexW1934430291MaRDI QIDQ2520595

Samir Siksek

Publication date: 16 December 2016

Published in: Algebra \& Number Theory (Search for Journal in Brave)

Abstract: A long-standing conjecture states that every positive integer other than 15, 22, 23, 50, 114, 167, 175, 186, 212, 231, 238, 239, 303, 364, 420, 428, 454 is a sum of at most seven positive cubes. This was first observed by Jacobi in 1851 on the basis of extensive calculations performed by the famous computationalist Zacharias Dase. We complete the proof of this conjecture, building on previous work of Linnik, Watson, McCurley, Ramar'e, Boklan, Elkies, and many others.

Full work available at URL: https://arxiv.org/abs/1505.00647

zbMATH Keywords

cubessums of cubesWaring

Mathematics Subject Classification ID

Waring's problem and variants (11P05)

Related Items (3)

Computers as a novel mathematical reality. II: Waring's problem ⋮ Power values of power sums: a survey ⋮ On multiplicative functions which are additive on positive cubes

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