Answer to Question #326602 in Combinatorics | Number Theory for Allen

Question

Prove that if 𝑎|𝑏 and 𝑏≠0, then |𝑎| ≤ |𝑏|.

Answer 1

$a|b\Rightarrow na=b\Rightarrow \left| b \right|=\left| na \right|=\left| n \right|\left| a \right|\\Since\,\,b\ne 0, n\ne 0\Rightarrow n\in \left\{ -1,1,-2,2,... \right\} \Rightarrow \left| n \right|\geqslant 1\\Then\\\left| b \right|\geqslant 1\cdot \left| a \right|=\left| a \right|$