The solution of $y^{2}+^{2n}=x^{3}$
HTML articles powered by AMS MathViewer
- by Stanley Rabinowitz
- Proc. Amer. Math. Soc. 62 (1977), 1-6
- DOI: https://doi.org/10.1090/S0002-9939-1977-0424678-9
- PDF | Request permission
Abstract:
All solutions to the diophantine equation \begin{equation}\tag {$\ast $}{y^2} + \gamma {2^n} = {x^3};\quad \gamma = \pm 1,\end{equation} are found.References
- A. I. Borevich and I. R. Shafarevich, Number theory, Pure and Applied Mathematics, Vol. 20, Academic Press, New York-London, 1966. Translated from the Russian by Newcomb Greenleaf. MR 0195803
- Robert D. Carmichael, The theory of numbers and Diophantine analysis, Dover Publications, Inc., New York, 1959. MR 0105381
- 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 L. Euler, Comm. Acad. Petrop. 10 (1738), 145; Comm. Arith. Coll. I, 33-34; Opera Omnia, (1), II, 56-58.
- Ove Hemer, On the solvability of the Diophantine equation $ax^2+by^2+cz^2=0$ in imaginary Euclidean quadratic fields, Ark. Mat. 2 (1952), 57โ82. MR 49917, DOI 10.1007/BF02591382 W. J. Le Veque, Topics in number theory, Vol. II, Addison-Wesley, Reading, Mass., 1961.
Bibliographic Information
- © Copyright 1977 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 62 (1977), 1-6
- MSC: Primary 10B25
- DOI: https://doi.org/10.1090/S0002-9939-1977-0424678-9
- MathSciNet review: 0424678