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The solution of $ 3y^2 \pm 2^n = x^3$


Author: Stanley Rabinowitz
Journal: Proc. Amer. Math. Soc. 69 (1978), 213-218
MSC: Primary 10B10
DOI: https://doi.org/10.1090/S0002-9939-1978-0480326-4
MathSciNet review: 0480326
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Abstract | References | Similar Articles | Additional Information

Abstract: The diophantine equation

$\displaystyle \quad 3{y^2} + {2^n}\gamma = {x^3},\quad {\text{with}}\;\gamma = \pm 1$ ($ \ast$)

is solved.

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

  • [1] O. Hemer, On the Diophantine equation $ {y^2} - k = {x^3}$, Thesis, Univ. of Uppsala, Almqvist & Wiksells, Uppsala, 1952. MR 14, 354.
  • [2] W. J. LeVeque, Topics in number theory, Vol. II, Addison-Wesley, Reading, Mass., 1961.
  • [3] S. Rabinowitz, The solution of $ {y^2} \pm {2^n} = {x^3}$, Proc. Amer. Math. Soc. 62 (1977), 1-6. MR 0424678 (54:12637)
  • [4] B. L. van der Waerden, Modern algebra, Vol. I, Ungar, New York, 1949.

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1978-0480326-4
Keywords: Ring of integers, norm
Article copyright: © Copyright 1978 American Mathematical Society

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