I have done many attempts of computations to get such integers $x, y, z$ for which $390=x^3+y^3+z^3$, but I can't however $390 \neq 4\bmod 9$ or $-4 \bmod 9$ which means there are solutions? Any help?
2026-04-01 22:38:50.1775083130
For which $x,y, z$ we have $390=x^3+y^3+z^3$ with $ x, y, z$ integers?
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It's actually an open problem. We still don't know whether numbers such as $114, 390, 579, 627, 633, 732, 906, 921$ and $975$ are the sum of $3$ cubes.