A note on the Diophantine equation 𝑥ⁿ+𝑦ⁿ+𝑧ⁿ=3

Scarowsky, Manny; Boyarsky, Abraham

doi:10.1090/S0025-5718-1984-0726000-9

Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

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A note on the Diophantine equation $x^{n}+y^{n}+z^{n}=3$
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by Manny Scarowsky and Abraham Boyarsky PDF

Math. Comp. 42 (1984), 235-237 Request permission

Abstract:

In this note solutions for the Diophantine equation \[ {x^3} + {y^3} + {z^3} = 3\] are sought along planes $x + y + z = 3m$, $m \in {\mathbf {Z}}$. This was done for $|m| \leqslant 50000$, and no new solutions were found.

References

L. J. Mordell, Diophantine equations, Pure and Applied Mathematics, Vol. 30, Academic Press, London-New York, 1969. MR 0249355
Alan Baker, Transcendental number theory, Cambridge University Press, London-New York, 1975. MR 0422171, DOI 10.1017/CBO9780511565977