Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)

 
 

 

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
DOI: https://doi.org/10.1090/S0025-5718-1969-0245513-1
MathSciNet review: 0245513
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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. Makowski, ``Sur quelques problèmes concernant les sommes de quatre cubes,'' Acta Arith., v. 5, 1959, pp. 121-123. MR 21 #5609. MR 0106879 (21:5609)
  • [3] A. Schinzel & W. Sierpiński, ``Sur les sommes de quatre cubes,'' Acta Arith., v. 4, 1958, pp. 20-30. MR 0095158 (20:1664)
  • [4] W. Sierpiński, A Selection of Problems in the Theory of Numbers, Macmillan, New York, 1964, p. 115. MR 30 #1078. MR 0170843 (30:1078)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 10.12

Retrieve articles in all journals with MSC: 10.12


Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1969-0245513-1
Article copyright: © Copyright 1969 American Mathematical Society

American Mathematical Society