Waring problem variant

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.

It is exactly what you'd expect from the name, Waring was watching Netflix with Goldbach, when they suddenly came up with this.