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, 48, 1
- Polynomial | 0, 608, 20
- Mathematics | 17, 30k, 679
- Ciro Santilli's Homepage | 262, 222k, 4k
- Undecidable problem | 148, 220, 3