[seqfan] Re: Is the set of numbers representable by sum of 5 positive cubes in exactly 3 ways finite?

[D. S. McNeil]

If we weaken positive cubes to nonnegative cubes, Deshouillers, Hennecart,
and Landreau (2000) give numerical and heuristic evidence that all numbers
past 7373170279850 are representable as the sum of 4 nonnegative cubes.

So if they're right, then eventually we can just take some N and represent
each of (N-1^3, N-2^3, N-3^3, N-4^3) as the sum of four cubes and then take
1^3, 2^3, 3^3, 4^3 as our fifth cube, giving at least four 5-cube
representations for N.

So I'd bet a fair amount that the set of numbers representable by the sum
of 5 positive cubes in exactly three ways is indeed finite.


Doug