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Let $n\ge 2$ be an integer and let $\mathbb F_q$ be the finite field with $q$elements, where $q$ is a prime power. Given $\mathbb F_q$-affine hyperplanes$\mathcal A_1, \ldots, \mathcal A_n$ of $\mathbb F_{q^n}$ in general position,we study the existence and distribution of primitive elements of $\mathbbF_{q^n}$, avoiding each $\mathcal A_i$. We obtain both asymptotic and concreteresults, relating to past works on digits over finite fields.

On primitive elements of finite fields avoiding affine hyperplanes