Triples of sixth powers with equal sums
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- by Simcha Brudno PDF
- Math. Comp. 30 (1976), 646-648 Request permission
Abstract:
The diophantine equation ${x^6} + {y^6} + {z^6} = {u^6} + {v^6} + {w^6}$ is shown to have a two-parameter solution which is homogeneous of degree four. The solution also satisfies ${x^2} + {y^2} + {z^2} = {u^2} + {v^2} + {w^2}$; and in addition, $3x + y + z = 3u + v + w$.References
- Simcha Brudno, On generating infinitely many solutions of the Diophantine equation $A^{6}+B^{6}+C^{6}=D^{6}+E^{6}+F^{6}$, Math. Comp. 24 (1970), 453โ454. MR 271020, DOI 10.1090/S0025-5718-1970-0271020-4
- Simcha Brudno and Irving Kaplansky, Equal sums of sixth powers, J. Number Theory 6 (1974), 401โ403. MR 371809, DOI 10.1016/0022-314X(74)90036-5
- G. H. Hardy and E. M. Wright, An introduction to the theory of numbers, Oxford, at the Clarendon Press, 1954. 3rd ed. MR 0067125
- L. J. Lander, T. R. Parkin, and J. L. Selfridge, A survey of equal sums of like powers, Math. Comp. 21 (1967), 446โ459. MR 222008, DOI 10.1090/S0025-5718-1967-0222008-0 K. SUBBA RAO, "On sums of sixth powers," J. London Math. Soc., v. 9, 1934, pp. 172-173.
Additional Information
- © Copyright 1976 American Mathematical Society
- Journal: Math. Comp. 30 (1976), 646-648
- MSC: Primary 10B15
- DOI: https://doi.org/10.1090/S0025-5718-1976-0406923-6
- MathSciNet review: 0406923