Common Ratio in Integer Geometric Sequence is Rational
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Theorem
Let $\sequence {a_k}$ be a geometric sequence whose terms are all integers.
Then the common ratio of $\sequence {a_k}$ is rational.
Proof
From Integers form Subdomain of Rationals it follows that $a_k \in \Q$ for all $0 \le k \le n$.
The result follows from Common Ratio in Rational Geometric Sequence is Rational.
$\blacksquare$