Answer to Question #323367 in Abstract Algebra for Edi

Question

Let a and b be integers. Prove that if a∣b, then an∣bn for all positive integers n.

Answer 1

$a|b\Rightarrow \frac{b}{a}\in \mathbb{N} \Rightarrow \frac{bn}{an}=\frac{b}{a}\in \mathbb{N} \Rightarrow an|bn$