Vol. 10, No. 10, 2016

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

Samir Siksek

Vol. 10 (2016), No. 10, 2093–2119
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, 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