Density and finiteness results on sums of fractions

Number fields and divisible groups via model theory

“…For the model-theoretic approaches, the reader might consult [1,4,8]. In [9], the second author and Sertbaş proved that a number field K is either Q or an imaginary quadratic fied if and only if Equation (1.1) has only finitely many non-degenerate solutions with coordinates in O K for all a 1 , ..., a k ∈ O K .…”

“…Motivated by the mentioned result of [9], we state our first theorem. has only finitely many non-degenerate solutions…”