4 ms·
What about zero? Can zero be the sum of three cubes? Actually, I read that somebody proved it can't be done, but the proof is too long to fit in this comment.
by alejohausner 7y ago
What about zero? Can zero be the sum of three cubes? Actually, I read that somebody proved it can't be done, but the proof is too long to fit in this comment. ;-)
- deleted 7y ago[deleted]
- 3JPLW 7y agoYes. 0³+0³+0³. Or x³+(-x)³+0³.
- FreeFull 7y agoFor this particular problem, none of the cubes are allowed to be 0
- OscarCunningham 7y agoI don't think that's a restriction that's usually enforced in this case. It seems nicer to allow the cubes to be zero since then the conjecture that the achievable sums are everything not 4 or 5 mod 9 can be stated without special cases.
- 3JPLW 7y agoYes. The joke the original commenter is playing is that Fermat's `x³ + y³ = z³` is equivalent to `x³ + y³ + (-z)³ = 0`.