Is it known what the smallest power is for which three summands are insufficient? Is there a smallest power? I imagine that would be hugely difficult, but for all I know it falls to the same methods as Fermat. (I'm no expert.)
Edit: I guess the answer might be "5" depending on what the paper means by "smallest" example. (smallest largest number vs smallest smallest number.)
Edit: I guess the answer might be "5" depending on what the paper means by "smallest" example. (smallest largest number vs smallest smallest number.)