Question Number 63499 by Rio Michael last updated on 04/Jul/19
$${given}\:{that}\:\:\:{a}\mid{b},\:{show}\:{that}\:−{a}\mid{b}. \\ $$
Answered by MJS last updated on 04/Jul/19
$${a}\mid{b}\:\Rightarrow\:\frac{{b}}{{a}}={c}\:\mathrm{with}\:{c}\in\mathbb{Z} \\ $$$$\Rightarrow\:−\frac{{b}}{{a}}=\left(−\mathrm{1}\right)\frac{{b}}{{a}}=\left(−\mathrm{1}\right){c}=−{c} \\ $$$${c}\in\mathbb{Z}\:\Leftrightarrow\:−{c}\in\mathbb{Z} \\ $$