www.jstor.org/stable/1970438 says for prime modulo there is an algorithm.
Question for non-prime modulo: math.stackexchange.com/questions/4944623/are-diophantine-equations-decidable-in-modular-arithmetic
TODO is it or is not:
- mathoverflow.net/questions/207482/algorithmic-un-solvability-of-diophantine-equations-of-given-degree-with-given
- math.stackexchange.com/questions/181380/second-degree-diophantine-equations
- mathoverflow.net/questions/142938/is-there-an-algorithm-to-solve-quadratic-diophantine-equations
- math.stackexchange.com/questions/798609/is-there-any-solution-to-this-quadratic-diophantine-equation
mathoverflow.net/questions/11540/what-are-the-most-attractive-turing-undecidable-problems-in-mathematics/103415#103415 provides a specific single undecidable Diophantine equation.
mathoverflow.net/questions/11540/what-are-the-most-attractive-turing-undecidable-problems-in-mathematics/11557#11557 contains a good overview of the decidability status of variants over rings other than the integers.
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