https://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.
https://mathoverflow.net/questions/11540/what-are-the-most-attractive-turing-undecidable-problems-in-mathematics/103415#103415 provides a specific undecidable equation over the integers with only one missing constant
- Diophantine equation | 12, 44, 1
- Polynomial | 0, 58, 6
- Mathematics | 17, 10k, 260
- Ciro Santilli's Homepage | 238, 154k, 2k
- Undecidable problem | 144, 212, 3