Arithmetic invariants are found which determine the index i ( K ) i(K) of a number field K K . They are used to obtain an explicit formula under certain restrictions on K K . They provide also a complete explanation of a phenomenon conjectured by Ore [ 8 {8} ] and showed by Engstrom in a particular case [ 2 {2} ].
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Enric Nart (1985) studied this question.
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