As far as I understand, the decidability of solvability of diophantine equations over the rationals is an open problem. What about the decidability of solvability over a given p-adic field?
2026-04-12 03:53:12.1775965992
Is solvability of diophantine equations over a p-adic field decidable?
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Decidable. Please see the very good survey article by Poonen.