給定了質數P和正整數n,這篇文章將探討有理數體Q的degree-n循環擴張且滿足P這個質理想是inert,這樣的擴張是否存在,當n是8的倍數時,我們將證明Q沒有degree-n的循環擴張滿足2這個質理想是inert.

Given a prime number p and an arbitrary nature number n, we discuss how to construct a degree-n cyclic extension E/Q such that pZ is inert. When 8 divides n, we prove that there is no degree-n cyclic extension E over Q such that 2Z is inert in E.

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