On a question of Mordell

Abstract

We make several improvements to methods for finding integer solutions to x3+ y3+ z3= 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 andWoollett in 1954 and resolves a challenge posed by Mordell in 1953.