> You need to find a mathematical reason why it can’t halt, and there’s no systematic method for finding such reasons—that was the great discovery of Gödel and Turing nearly a century ago.
That's only true for sufficiently large N, large enough to encode the halting paradox. (How large is that N? It's larger than 5!) Smaller N can and do fall to systematic methods.
> (x) = (5x+18)/3 if x = 0 (mod 3),
The second = should be \equivalent. This is a rare case where that actually matters, because is being used in both non-modular integer operations (divide by 3) and modular operations (where division by 3 is not defined).
> You need to find a mathematical reason why it can’t halt, and there’s no systematic method for finding such reasons—that was the great discovery of Gödel and Turing nearly a century ago.
That's only true for sufficiently large N, large enough to encode the halting paradox. (How large is that N? It's larger than 5!) Smaller N can and do fall to systematic methods.
> (x) = (5x+18)/3 if x = 0 (mod 3),
The second = should be \equivalent. This is a rare case where that actually matters, because is being used in both non-modular integer operations (divide by 3) and modular operations (where division by 3 is not defined).