{tag=Open problem in mathematics}
{title2=Every number has infinitely many representations as the sum of three cubes}
{wiki}

Compared to <Waring's problem>, this is potentially much harder, as we can go infinitely negative in our attempts, there isn't a bound on how many tries we can have for each number.

In other words, it is unlikely to have a <Conjecture reduction to a halting problem>.

\Video[https://www.youtube.com/watch?v=GXhzZAem7k0]
{title=3 as the sum of the 3 cubes by <Numberphile> (2019)}


Sum of three cubes

ID: sum-of-three-cubes