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by Ciro Santilli (@cirosantilli, 37)

Sum of three cubes (Every number has infinitely many representations as the sum of three cubes)

 ... Additive number theory Additive basis Additive basis theorem Waring's problem Waring problem variant Waring problem with negative numbers allowed
 0 By others on same topic  0 Discussions  Updated 2025-05-26  +Created 1970-01-01  See my version
Tags: Open problem in mathematics
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 1.
3 as the sum of the 3 cubes by Numberphile (2019)
Source.

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