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On generating infinitely many solutions of the Diophantine equation $ A\sp{6}+B\sp{6}+C\sp{6}=D\sp{6}+E\sp{6}+F\sp{6}$


Author: Simcha Brudno
Journal: Math. Comp. 24 (1970), 453-454
MSC: Primary 10.13
DOI: https://doi.org/10.1090/S0025-5718-1970-0271020-4
Corrigendum: Math. Comp. 25 (1971), 409.
Corrigendum: Math. Comp. 25 (1971), 409.
MathSciNet review: 0271020
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Abstract | References | Similar Articles | Additional Information

Abstract: A method of generating infinitely many solutions of the Diophantine equation $ {A^6} + {B^6} + {C^6} = {D^6} + {E^6} + {F^6}$is presented. The technique is to reduce the equation to one of fourth degree and to use the known recursive solutions to the fourth-order equations.


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

  • [1] V. A. Lebesgue, "Résolution des équations biquadratiques: (1)(2) $ {z^2} = {x^4} \pm {2^m}{y^4}$, $ {z^2} = {2^m}{x^4} - {y^4}$. (4)(5) $ {2^m}{z^2} = {x^4} \pm {y^4}$," J. Math. Pures Appl. (1), v. 18, 1853, pp. 73-86.
  • [2] L. E. Dickson, History of the Theory of Numbers. Vol. II, Chelsea, New York, 1952. Chapter XXII. p. 637.
  • [3] L. J. Lander, T. R. Parkin & J. L. Selfridge, "A survey of equal sums of like powers." Math. Comp., v. 21. 1967. pp. 446-459. MR 36 #5060. MR 0222008 (36:5060)
  • [4] A. Desboves, "Mémoire sur la résolution en nombres entiers de l'équation $ a{X^4} + b{Y^4} = c{Z^n}$." Nouvelles Ann. Math. (2). v. 18, 1879, pp. 265-279, 398-410, 433-444, 481-499.

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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1970-0271020-4
Keywords: Diophantine equation, fourth-order equations, sixth degree equations
Article copyright: © Copyright 1970 American Mathematical Society

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