Let $α$ be an element of $\mathbb F_q$ with largest order $t$ . Show that set of elements with order dividing $t$ should have cardinality $t$

Question

Let $α$ be an element of $\mathbb F_q$ with largest order $t$ . Show that set of elements with order dividing $t$ should have cardinality $t$, so there must be some non-zero element $γ ∈ \mathbb F_q$ with $a = ord(γ)$ not dividing $t$.

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