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

How to cite


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>.

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},

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 -


  1. 1 Birch, B.J. and Swinnerton-Dyer, H.P.F.: Notes on elliptic curves I, Crelle212, Heft 1/2 (1963) 7-25. Zbl0118.27601MR146143
  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

NotesEmbed ?


You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.


Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.