First Element of Geometric Sequence not dividing Second

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

Let $a_0$ not be a divisor of $a_1$.

Then:
 * $\forall j, k \in \set {0, 1, \ldots, n}, j \ne k: a_j \nmid a_k$

That is, if the initial term of $P$ does not divide the second, no term of $P$ divides any other term of $P$.