Journal
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
Volume 118, Issue 11, Pages -Publisher
NATL ACAD SCIENCES
DOI: 10.1073/pnas.2022377118
Keywords
Diophantine equations; Hilbert's tenth problem; sums of three cubes
Categories
Funding
- Simons Foundation [550033]
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The research team made improvements to methods for finding integer solutions to x(3) + y(3) + z(3) = k for small values of k and implemented these on Charity Engine's global compute grid of 500,000 volunteer PCs, finding new representations for several values of k, including 3 and 42. This completes a search initiated in 1954 and resolves a challenge posed in 1953.
We make several improvements to methods for finding integer solutions to x(3) + y(3) + z(3) = k 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.
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