Matiyasevich 1970 (building on Davis-Putnam-Robinson 1961): every r.e. set has a Diophantine representation, so deciding integer solvability of polynomial equations is reducible to — and equivalent to — the halting problem.
Matiyasevich 1970 (building on Davis-Putnam-Robinson 1961): every r.e. set has a Diophantine representation, so deciding integer solvability of polynomial equations is reducible to — and equivalent to — the halting problem.