Triples of sixth powers with equal sums

Author:
Simcha Brudno

Journal:
Math. Comp. **30** (1976), 646-648

MSC:
Primary 10B15

DOI:
https://doi.org/10.1090/S0025-5718-1976-0406923-6

MathSciNet review:
0406923

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Abstract | References | Similar Articles | Additional Information

Abstract: The diophantine equation is shown to have a two-parameter solution which is homogeneous of degree four. The solution also satisfies ; and in addition, .

**[1]**Simcha Brudno,*On generating infinitely many solutions of the Diophantine equation 𝐴⁶+𝐵⁶+𝐶⁶=𝐷⁶+𝐸⁶+𝐹⁶*, Math. Comp.**24**(1970), 453–454. MR**0271020**, https://doi.org/10.1090/S0025-5718-1970-0271020-4**[2]**Simcha Brudno and Irving Kaplansky,*Equal sums of sixth powers*, J. Number Theory**6**(1974), 401–403. MR**0371809**, https://doi.org/10.1016/0022-314X(74)90036-5**[3]**G. H. Hardy and E. M. Wright,*An introduction to the theory of numbers*, Oxford, at the Clarendon Press, 1954. 3rd ed. MR**0067125****[4]**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**[5]**K. SUBBA RAO, "On sums of sixth powers,"*J. London Math. Soc.*, v. 9, 1934, pp. 172-173.

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DOI:
https://doi.org/10.1090/S0025-5718-1976-0406923-6

Article copyright:
© Copyright 1976
American Mathematical Society