I can also implement compliant IEEE 754 floating point arithmetic, with all rounding modes and exceptions, in Conway’s Game of Life, and I can implement that on a Turing machine and emulate that Turing machine in Brainfuck. This does not mean it’s sensible — it would be a serious engineering project that should be decomposed, built in pieces, and tested or verified in pieces. Which even a Chinese LLM ought to be able to do in an appropriate environment with appropriate resources and an appropriate prompt.

But that is not what this is testing. And I’m not even sure which number system the mentioned roots of unity are in. Maybe it’s supposed to be generic over number systems in a delightfully untyped lambda calculus sort of way?

edit: after pasting the entire problem including the solution, ChatGPT is able to explain “GN numbers”. I suspect its explanation is sort of correct. But I get no web search results for GN numbers and I can’t really tell whether ChatGPT is giving a semi-hallucinated description or figuring it out from the problem and its solution or what.

Lambda calculus people have the phrase "adequate numeral system" because they've discovered many different numeral systems.