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.
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3 as the sum of the 3 cubes by Numberphile (2019)
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  1. Waring problem with negative numbers allowed
  2. Waring problem variant
  3. Waring's problem
  4. Additive basis theorem
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  6. Additive number theory
  7. Diophantine equation
  8. Polynomial
  9. Numeric function
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