For every quadratic field K, deciding solvability of polynomial equations in 16 variables over its ring of integers is undecidable, and 15 variables suffice when K is real quadratic.
Robinson,Reduction of an arbitrary diophantine equation to one in 13 unknowns, Acta Arith.27(1975), 521–553
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On Diophantine equations over the integer rings of quadratic fields
For every quadratic field K, deciding solvability of polynomial equations in 16 variables over its ring of integers is undecidable, and 15 variables suffice when K is real quadratic.