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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The solution of $ y\sp{2}+\sp{2n}=x\sp{3}$


Author: Stanley Rabinowitz
Journal: Proc. Amer. Math. Soc. 62 (1977), 1-6
MSC: Primary 10B25
MathSciNet review: 0424678
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Abstract | References | Similar Articles | Additional Information

Abstract: All solutions to the diophantine equation

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

are found.

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

  • [1] A. I. Borevich and I. R. Shafarevich, Number theory, Translated from the Russian by Newcomb Greenleaf. Pure and Applied Mathematics, Vol. 20, Academic Press, New York-London, 1966. MR 0195803 (33 #4001)
  • [2] Robert D. Carmichael, The theory of numbers and Diophantine analysis, Dover Publications, Inc., New York, 1959. MR 0105381 (21 #4123)
  • [3] B. N. Delone and D. K. Faddeev, The theory of irrationalities of the third degree, Translations of Mathematical Monographs, Vol. 10, American Mathematical Society, Providence, R.I., 1964. MR 0160744 (28 #3955)
  • [4] L. Euler, Comm. Acad. Petrop. 10 (1738), 145; Comm. Arith. Coll. I, 33-34; Opera Omnia, (1), II, 56-58.
  • [5] Ove Hemer, On the solvability of the Diophantine equation 𝑎𝑥²+𝑏𝑦²+𝑐𝑧²=0 in imaginary Euclidean quadratic fields, Ark. Mat. 2 (1952), 57–82. MR 0049917 (14,247d)
  • [6] W. J. Le Veque, Topics in number theory, Vol. II, Addison-Wesley, Reading, Mass., 1961.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1977-0424678-9
PII: S 0002-9939(1977)0424678-9
Keywords: Diophantine equation, ring of integers, class number, unique factorization domain, greatest common divisor
Article copyright: © Copyright 1977 American Mathematical Society



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