Color each Gaussian integer in the complex plane according to the number of ways it can be expressed as the sum of the cubes of two Gaussian integers. What does the pattern look like? For a given Gaussian integer, is there a limit to the search space needed to be sure you have found all the possible ways it can be expressed as the sum of cubes?
Repeat with Eisenstein integers. Repeat with other powers, a square plus a cube, etc.
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