We give sufficient conditions for any linear combination over ℚ of numbers ∑n=1∞b1,n∕α1,n,…,∑n=1∞bK,n∕αK,n to have algebraic degree greater than an arbitrary fixed integer D when the numbers αi,n are algebraic integers of sufficiently rapidly increasing modulus and the bi,n are positive integers that are not too large.
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Mathias L. Laursen (2023) studied this question.