= Sum of three cubes
{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)}