On generating infinitely many solutions of the Diophantine equation

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 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.

**[1]**V. A. Lebesgue, "Résolution des équations biquadratiques: (1)(2) , . (4)(5) ,"*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, and J. L. Selfridge,*A survey of equal sums of like powers*, Math. Comp.**21**(1967), 446–459. MR**0222008**, https://doi.org/10.1090/S0025-5718-1967-0222008-0**[4]**A. Desboves, "Mémoire sur la résolution en nombres entiers de l'équation ."*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