On generating infinitely many solutions of the Diophantine equation $A^{6}+B^{6}+C^{6}=D^{6}+E^{6}+F^{6}$
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- by Simcha Brudno PDF
- Math. Comp. 24 (1970), 453-454 Request permission
Corrigendum: Math. Comp. 25 (1971), 409.
Corrigendum: Math. Comp. 25 (1971), 409.
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
- 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.
L. E. Dickson, History of the Theory of Numbers. Vol. II, Chelsea, New York, 1952. Chapter XXII. p. 637.
- L. J. Lander, T. R. Parkin, and J. L. Selfridge, A survey of equal sums of like powers, Math. Comp. 21 (1967), 446–459. MR 222008, DOI 10.1090/S0025-5718-1967-0222008-0 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.
Additional Information
- © Copyright 1970 American Mathematical Society
- Journal: Math. Comp. 24 (1970), 453-454
- MSC: Primary 10.13
- DOI: https://doi.org/10.1090/S0025-5718-1970-0271020-4
- MathSciNet review: 0271020