On the sum of consecutive cubes being a perfect square

R. J. Stroeker

Compositio Mathematica (1995)

  • Volume: 97, Issue: 1-2, page 295-307
  • ISSN: 0010-437X

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Stroeker, R. J.. "On the sum of consecutive cubes being a perfect square." Compositio Mathematica 97.1-2 (1995): 295-307. <http://eudml.org/doc/90381>.

@article{Stroeker1995,
author = {Stroeker, R. J.},
journal = {Compositio Mathematica},
keywords = {sum of consecutive cubes; integral points of an elliptic curve; LLL- reduction; perfect square; linear forms in elliptic logarithms},
language = {eng},
number = {1-2},
pages = {295-307},
publisher = {Kluwer Academic Publishers},
title = {On the sum of consecutive cubes being a perfect square},
url = {http://eudml.org/doc/90381},
volume = {97},
year = {1995},
}

TY - JOUR
AU - Stroeker, R. J.
TI - On the sum of consecutive cubes being a perfect square
JO - Compositio Mathematica
PY - 1995
PB - Kluwer Academic Publishers
VL - 97
IS - 1-2
SP - 295
EP - 307
LA - eng
KW - sum of consecutive cubes; integral points of an elliptic curve; LLL- reduction; perfect square; linear forms in elliptic logarithms
UR - http://eudml.org/doc/90381
ER -

References

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  2. 2 Bremner, A.: On the Equation Y2 = X(X2 + p), in: "Number Theory and Applications " (R. A. Mollin, ed.), Kluwer, Dordrecht, 1989,3-23. Zbl0689.14010MR1123066
  3. 3 Bremner, A. and Cassels, J.W.S.: On the Equation Y2 = X(X2 + p), Math. Comp.42 (1984) 257-264. Zbl0531.10014MR726003
  4. 4 Cassels, J.W.S.: A Diophantine Equation, Glasgow Math. J.27 (1985) 11-18. Zbl0576.10010MR819824
  5. 5 Cremona, J.E.: "Algorithms for Modular Elliptic Curves", Cambridge University Press, 1992. Zbl0758.14042MR1201151
  6. 6 David, S.: Minorations de formes linéaires de logarithmes elliptiques, Publ. Math. de l'Un. Pierre et Marie Curie no. 106, Problèmes diophantiens 1991-1992, exposé no. 3. 
  7. 7 Dickson, L.E.: "History of the Theory of Numbers", Vol. II: "Diophantine Analysis", Chelsea Publ. Co. 1971 (first published in 1919 by the Carnegie Institute of Washington, nr. 256). MR245500JFM47.0100.04
  8. 8 Gebel, J., Pethö, A. and Zimmer, H.G.: Computing Integral Points on Elliptic Curves, Acta Arithm., 68 (2) (1994) 171-192. Zbl0816.11019MR1305199
  9. 9 Knapp, Anthony W.: "Elliptic Curves", Math. Notes40, Princeton University Press, 1992. Zbl0804.14013MR1193029
  10. 10 Koblitz, N.: "Introduction to Elliptic Curves and Modular Forms", Springer-Verlag, New York etc., 1984. Zbl0553.10019MR766911
  11. 11 Silverman, Joseph H.: "The Arithmetic of Elliptic Curves", GTM 106, Springer-Verlag, New York etc., 1986. Zbl0585.14026MR817210
  12. 12 Silverman, J.H.: Computing Heights on Elliptic Curves, Math. Comp.51 (1988) 339-358. Zbl0656.14016MR942161
  13. 13 Silverman, J.H.: The difference between the Weil height and the canonical height on elliptic curves, Mat. Comp.55 (1990) 723-743. Zbl0729.14026MR1035944
  14. 14 Silverman, Joseph H. and Tate, John: "Rational Points on Elliptic Curves", UTM, Springer-Verlag, New York etc., 1992. Zbl0752.14034MR1171452
  15. 15 Stroeker, Roel J. and Top, Jaap: On the Equation Y2 = (X + p)(X2 + p2), Rocky Mountain J. Math.24 (3) (1994) 1135-1161. Zbl0810.11038MR1307595
  16. 16 Stroeker, R.J. and Tzanakis, N.: On the Application of Skolem's p-adic Method to the solution of Thue Equations, J. Number Th.29 (2) (1988) 166-195. Zbl0674.10012MR945593
  17. 17 Stroeker, R.J. and Tzanakis, N.: Solving elliptic diophantine equations by estimating linear forms in elliptic logarithms, Acta Arithm.67 (2) (1994) 177-196. Zbl0805.11026MR1291875
  18. 18 Stroeker, Roel J. and De Weger, Benjamin M. M.: On Elliptic Diophantine Equations that Defy Thue's Method - The Case of the Ochoa Curve, Experimental Math., to appear. Zbl0824.11012
  19. 19 Tate, J.: Variation of the canonical height of a point depending on a parameter, American J. Math.105 (1983) 287-294. Zbl0618.14019MR692114
  20. 20 Tzanakis, N. and De Weger, B.M.M.: On the Practical Solution of the Thue Equation, J. Number Th.31 (2) (1989) 99-132. Zbl0657.10014MR987566
  21. 21 De Weger, B.M.M.: "Algorithms for Diophantine Equations", CWI Tract65, Stichting Mathematisch centrum, Amsterdam1989. Zbl0687.10013MR1026936
  22. 22 Zagier, D.: Large Integral Points on Elliptic Curves, Math. Comp.48 (1987) 425-436. Zbl0611.10008MR866125

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