Undecidable Diophantine equation example by 
Ciro Santilli 34 Updated 2024-12-15 +Created 1970-01-01
Ciro Santilli 34 Updated 2024-12-15 +Created 1970-01-01mathoverflow.net/questions/11540/what-are-the-most-attractive-turing-undecidable-problems-in-mathematics/103415#103415 provides a specific single undecidable Diophantine equation.