Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

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

 
 

 

Which integers are representable as the product of the sum of three integers with the sum of their reciprocals?


Authors: Andrew Bremner, Richard K. Guy and Richard J. Nowakowski
Journal: Math. Comp. 61 (1993), 117-130
MSC: Primary 11D25; Secondary 11G05, 11G40
DOI: https://doi.org/10.1090/S0025-5718-1993-1189516-5
MathSciNet review: 1189516
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: For example, the integer 564 is so representable by the three integers 122 44200 50100028778116351171 17995213613513491867, -3460 69586 84255 04865 64589 22621 88752 08971 30654 24460 and 74807 1910153025 27837945836017146464 94820 59055 28060.


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

  • [1] B. J. Birch and H. P. F. Swinnerton-Dyer, Notes on elliptic curves. II, J. Reine Angew. Math. 218 (1965), 79-108. MR 0179168 (31:3419)
  • [2] Andrew Bremner, A geometric approach to equal sums of sixth powers, Proc. London Math. Soc. (3) 43 (1981), 544-581. MR 635569 (83g:14018)
  • [3] J. W. S. Cassels, W. J. Ellison, and A. Pfister, On sums of squares and on elliptic curves over function fields, J. Number Theory 3 (1971), 125-149. MR 0292781 (45:1863)
  • [4] L. J. Mordell, Diophantine equations, Academic Press, New York, 1969. MR 0249355 (40:2600)
  • [5] J. H. Silverman, The arithmetic of elliptic curves, Springer-Verlag, New York, 1986. MR 817210 (87g:11070)
  • [6] D. Zagier and G. Kramarz, Numerical investigation related to the L-series of certain elliptic curves, J. Indian Math. Soc. 52 (1987), 51-69. MR 989230 (90d:11072)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 11D25, 11G05, 11G40

Retrieve articles in all journals with MSC: 11D25, 11G05, 11G40


Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1993-1189516-5
Article copyright: © Copyright 1993 American Mathematical Society

American Mathematical Society