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Mathematics of Computation

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A note on sums of four cubes

Authors: M. Lal, W. Russell and W. J. Blundon
Journal: Math. Comp. 23 (1969), 423-424
MSC: Primary 10.12
MathSciNet review: 0245513
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Abstract: A search for the integral solutions of the Diophantine equation $ {x^3} + {y^3} + 2{z^3} = k$ for $ \vert x\vert$ $ \vert y\vert$ and $ \vert z\vert < {10^5}$ was made on an I.B.M. 1620 Model 1. These results showed that there are now just 19 values of $ k$ in the range $ 1 \leqq k \leqq 999$ for which no solution is known.

References [Enhancements On Off] (What's this?)

  • [1] C. Ko, ``Decompositions into four cubes,'' J. London Math. Soc., v. 11, 1936, pp. 218-219.
  • [2] A. Mąkowski, Sur quelques problèmes concernant les sommes de quatre cubes, Acta Arith. 5 (1959), 121–123 (French). MR 0106879
  • [3] A. Schinzel and W. Sierpiński, Sur les sommes de quatre cubes, Acta Arith. 4 (1958), 20–30 (French). MR 0095158
  • [4] Wacław Sierpiński, A selection of problems in the theory of numbers, Translated from the Polish by A. Sharma. A Pergamon Press Book, The Macmillan Co., New York, 1964. MR 0170843

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Article copyright: © Copyright 1969 American Mathematical Society