First Element of Geometric Sequence not dividing Second

Theorem
Let $P = \left\langle{a_j}\right\rangle_{1 \mathop \le j \mathop \le n}$ be a geometric progression of integers of length $n$.

Let $a_1$ not be a divisor of $a_2$.

Then:
 * $\forall j, k \in \left\{{1, 2, \ldots, n}\right\}, j \ne k: a_j \nmid a_k$

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