On a question of Mordell

Andrew R Booker; Andrew V Sutherland

doi:10.1073/pnas.2022377118

On a question of Mordell

Proc Natl Acad Sci U S A. 2021 Mar 16;118(11):e2022377118. doi: 10.1073/pnas.2022377118.

Authors

Andrew R Booker¹, Andrew V Sutherland²

Affiliations

¹ School of Mathematics, University of Bristol, Bristol BS8 1UG, United Kingdom; Andrew.Booker@bristol.ac.uk drew@math.mit.edu.
² Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139 Andrew.Booker@bristol.ac.uk drew@math.mit.edu.

Abstract

We make several improvements to methods for finding integer solutions to [Formula: see text] for small values of k. We implemented these improvements on Charity Engine's global compute grid of 500,000 volunteer PCs and found new representations for several values of k, including 3 and 42. This completes the search begun by Miller and Woollett in 1954 and resolves a challenge posed by Mordell in 1953.

Keywords: Diophantine equations; Hilbert’s tenth problem; sums of three cubes.

Publication types

Research Support, Non-U.S. Gov't