In this paper, a new criterion is given to determine the p–rationality of some complex cubic number fields in terms of p–divisibility of certain terms of a third-order recurrence sequence, several illustrated examples are constructed, the relations between generalized abc–conjecture and the p–rationality are discussed, from which some explicit fields satisfying Greenberg’s Generalized Conjecture (GGC, for short) are obtained.
Li et al. (Thu,) studied this question.
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