New integer representations as the sum of three cubes

Beck, Michael; Pine, Eric; Tarrant, Wayne; Jensen, Kim

doi:10.1090/S0025-5718-07-01947-3

New integer representations as the sum of three cubes
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by Michael Beck, Eric Pine, Wayne Tarrant and Kim Yarbrough Jensen PDF

Math. Comp. 76 (2007), 1683-1690 Request permission

Abstract:

We describe a new algorithm for finding integer solutions to $x^3 + y^3 + z^3 = k$ for specific values of $k$. We use this to find representations for values of $k$ for which no solution was previously known, including $k=30$ and $k=52$.

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