For q = 3r (r ∈ ℕ), denote by 𝔽q the finite field of order q and for a positive integer m ≥ 2, let 𝔽qm be its extension field of degree m. We establish a sufficient condition for existence of a primitive normal element α such that f(α) is a primitive element, where f(x) = ax2 + bx + c, with a,b,c ∈ 𝔽qm satisfying b2≠ac in 𝔽qm.

中文翻译：

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有限域上二次型本原正规元的存在

为了q = 3r(r ∈ ℕ)，表示为𝔽q有限序域q对于一个正整数米 ≥ 2， 让𝔽q米是其学位的外延领域米. 我们建立了一个原始正常元素存在的充分条件α这样F(α)是一个原始元素，其中F(X) = 一种X2 + bX + C， 和一种,b,C ∈ 𝔽q米令人满意的b2≠一种C在𝔽q米.