Let [Formula: see text] be integers and [Formula: see text] be any prime power [Formula: see text] such that [Formula: see text]. We say that the extension [Formula: see text] possesses the line property for [Formula: see text]-primitive elements if, for every [Formula: see text], such that [Formula: see text], there exists some [Formula: see text], such that [Formula: see text] has multiplicative order [Formula: see text]. Likewise, if, in the above definition, [Formula: see text] is restricted to the value [Formula: see text], we say that [Formula: see text] possesses the translate property. In this paper, we take [Formula: see text] (so that necessarily [Formula: see text] is odd) and prove that [Formula: see text] possesses the translate property for 2-primitive elements unless [Formula: see text]. With some additional theoretical and computational effort, we show also that [Formula: see text] possesses the line property for 2-primitive elements unless [Formula: see text].

中文翻译：

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二次扩展中 2 基元元素的 translate 和 line 属性

令 [Formula: see text] 为整数， [Formula: see text] 为任意素数 [Formula: see text] 使得 [Formula: see text]。我们说扩展 [Formula: see text] 拥有 [Formula: see text]-原始元素的 line 属性，如果对于每个 [Formula: see text]，使得 [Formula: see text] 存在一些 [Formula: see text] : 见正文]，使得 [公式：见正文] 具有乘法顺序 [公式：见正文]。同样，如果在上面的定义中，[Formula: see text] 被限制为 [Formula: see text] 的值，我们说 [Formula: see text] 拥有 translate 属性。在本文中，我们取 [Formula: see text]（因此 [Formula: see text] 必然是奇数）并证明 [Formula: see text] 具有 2-primitive 元素的 translate 属性，除非 [Formula: see text] .