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

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, Ramaré, Boklan, Elkies, and many others.

Keywords

Waring, cubes, sums of cubes

Mathematical Subject Classification 2010

Primary: 11P05

Supplementary material

Magma scripts for the verification of the computations described in this paper, with their output (260 Mbytes)

Milestones

Received: 6 January 2016

Revised: 21 August 2016

Accepted: 23 September 2016

Published: 9 December 2016

Authors

Samir Siksek
Mathematics Institute University of Warwick Coventry CV4 7AL United Kingdom

Vol. 10, No. 10, 2016

Samir Siksek

Abstract

Keywords

Mathematical Subject Classification 2010

Supplementary material

Milestones

Authors