Geodesic
Variations on the theme of Hilbert's theorem 90
Glasgow mathematical journal, Tome 44 (2002) no. 3, pp. 435-441

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DOI

Given a number field K, we find two simple separate necessary and sufficient conditions on a given algebraic number for it to be expressible as a quotient (respectively as a difference) of two algebraic numbers conjugate over K. 
Dubickas, A.; Smyth, C. J. Variations on the theme of Hilbert's theorem 90. Glasgow mathematical journal, Tome 44 (2002) no. 3, pp. 435-441. doi: 10.1017/S0017089502030082
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