Direct consequence of Euclid's formula.

A generalization of the Pythagorean triple infinity question.

Once you hear about the uncomputability of such problems, it makes you see that all Diophantine equation questions risk being undecidable, though in some simpler cases we manage to come up with answers. The feeling is similar to watching people trying to solve the Halting problem, e.g. in the effort to determine BB(5).

mathoverflow.net/questions/11540/what-are-the-most-attractive-turing-undecidable-problems-in-mathematics/103415#103415 provides a specific single undecidable Diophantine equation.

And when it can't, attempt to classify which subset of the integers can be reached. E.g. Legendre's three-square theorem.

4 squares are sufficient by Lagrange's four-square theorem.

3 is not enough by Legendre's three-square theorem.

The subsets reachable with 2 and 3 squares are fully characterized by Legendre's three-square theorem.

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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.

The concept is a strong part of Water Margin.

The very first chapter opens with Grand Commander Hou disrespecting spirits by opening up a sealed tomb and unintentionally releasing 108 demons who presumably reincarnate as humans, a backstory to the events that follow years later.

This is well shown in the Japanese The Water Margin, but is skipped in the Chinese The Water Margin unfortunately.

The concept is also central to the Suikoden video game.

Actually, now that Ciro Santilli thinks about it, these were already likely meant as a "collectible" element by the author of the original book, as is strongly suggested by all the little illustrations of each character present on the Wikipedia page. Just like e.g. Catholic saints. It's Pokemon, but 2000 years earlier.

Ciro would notably feel many years later, that as he met random people online who were interested in improving eduction, or was otherwise networking to reach his goals, as if he were actually building up his 108 stars of destiny.

A central part, and perhaps the most interesting part of the novel, is how each character has been motivated by injustice to join the rebellion. This reminds Ciro of Final Fantasy VI