Triples of sixth powers with equal sums

Brudno, Simcha

doi:10.1090/S0025-5718-1976-0406923-6

Triples of sixth powers with equal sums
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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), 453–454. 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), 401–403. 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), 446–459. MR 222008, DOI 10.1090/S0025-5718-1967-0222008-0

J. London Math. Soc.