Divisibility of Elements of Geometric Sequence from One where First Element is Prime

Theorem
Let $Q_n = \sequence {a_j}_{0 \mathop \le j \mathop \le n}$ be a geometric sequence of length $n$ consisting of integers only.

Let $a_0 = 1$.

Let $a_1$ be a prime number.

Then the only divisors of $a_n$ are $a_j$ for $j \in \set {1, 2, \ldots, n}$.

Proof
From Form of Geometric Sequence of Integers from One, the elements of $Q_n$ are given by:
 * $Q_n = \tuple {1, a, a^2, \ldots, a^n}$

From Divisors of Power of Prime, each of $a_j$ for $j \in \set {1, 2, \ldots, n}$ are the only divisors of $a_n$.