Vol. 10, No. 10, 2016

Download this article
Download this article For screen
For printing
Recent Issues

Volume 14
Issue 10, 2575–2813
Issue 9, 2295–2574
Issue 8, 2001–2294
Issue 7, 1669–1999
Issue 6, 1331–1667
Issue 5, 1055–1329
Issue 4, 815–1054
Issue 3, 545–813
Issue 2, 275–544
Issue 1, 1–274

Volume 13, 10 issues

Volume 12, 10 issues

Volume 11, 10 issues

Volume 10, 10 issues

Volume 9, 10 issues

Volume 8, 10 issues

Volume 7, 10 issues

Volume 6, 8 issues

Volume 5, 8 issues

Volume 4, 8 issues

Volume 3, 8 issues

Volume 2, 8 issues

Volume 1, 4 issues

The Journal
About the Journal
Editorial Board
Editors’ Interests
Subscriptions
 
Submission Guidelines
Submission Form
Policies for Authors
Ethics Statement
 
ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Author Index
To Appear
 
Other MSP Journals
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