On solving the diophantine equation x3+ y3+z3= k on a vector computer

Mathematics of Computation

Volumn 61, Issue 203, 1993, Pages 235-244

  Heath Brown, D R ^a   Lioen, W M ^b   Te Riele, H J ^b  

^a MAGDALEN COLLEGE   (United Kingdom)

^b CWI   (Netherlands)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84966229015     PISSN: 00255718     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0025-5718-1993-1202610-5     Document Type: Article

References (9)

1. J. W. S. Cassels, The rational solutions of the Diophantine equation Y2 = X3 - D, Acta Math. 82(1950), 243-273.
2. V. L. Gardiner, R. B. Lazarus, and P. R. Stein, Solutions of the Diophantine equation x3+y3 = z3 - d, Math. Comp. 18 (1964), 408-413.
3. D. R. Heath-Brown, Searching for solutions of x3 + y3 + z3 = k, Sém. Théoriedes Nombres, Paris 1989-1990 (D. Sinnou, ed.), Birkhäuser, Boston, 1992, pp. 71-76.
4. Donald E. Knuth, The art of computer programming. Vol. 2. Seminumerical algorithms, Addison-Wesley, Reading, MA, 1981.
5. D. H. Lehmer, On the Diophantine equation x3 + y3 + z3 = 1, J. London Math. Soc. 31 (1956), 275-280.
6. J. C. P. Miller and M. F. C. Woollen, Solutions of the Diophantine equation x3+y3+z3 = k. J. London Math. Soc. 30 (1955), 101-110.
7. L. J. Mordell, On an infinity of integer solutions of ax3 + ar3 + bz3 = bc3, J. London Math. Soc. 30(1955), 111-113.
8. M. Scarowsky and A. Boyarsky, A note on the Diophantine equation x3 + y3 +z3 = 3. Math. Comp. 42 (1984), 235-237.
9. J. J. F. M. Schlichting, Double precision BLAS, Algorithms and Applications on Vector and Parallel Computers (H. J. J. te Riele, Th. J. Dekker, and H. A. van der Vorst. eds.), North-Holland, Amsterdam, 1987, pp. 229-249.