A note on the Diophantine equation 𝑥³+𝑦³+𝑧³=3

Cassels, J. W. S.

doi:10.1090/S0025-5718-1985-0771049-4

Mathematics of Computation

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A note on the Diophantine equation $x^ 3+y^ 3+z^ 3=3$
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by J. W. S. Cassels PDF

Math. Comp. 44 (1985), 265-266 Request permission

Abstract:

Any integral solution of the title equation has $x \equiv y \equiv z$ (9).

References

J. Reine Angew. Math.

L. J. Mordell, On the integer solutions of the equation $x^2+y^2+z^2+2xyz=n$, J. London Math. Soc. 28 (1953), 500–510. MR 56619, DOI 10.1112/jlms/s1-28.4.500
Manny Scarowsky and Abraham Boyarsky, A note on the Diophantine equation $x^{n}+y^{n}+z^{n}=3$, Math. Comp. 42 (1984), no. 165, 235–237. MR 726000, DOI 10.1090/S0025-5718-1984-0726000-9