Question Number 11214 by uni last updated on 17/Mar/17
Answered by FilupS last updated on 17/Mar/17
$${a}+\frac{{b}}{{a}}=\mathrm{4}\:\:\Rightarrow\:\:{b}={a}\left(\mathrm{4}−{a}\right) \\ $$$$\because{a}\in\mathbb{Z}\:\:\mathrm{and}\:\:\mathrm{RHS}\in\mathbb{Z},\:\therefore{b}\in\mathbb{Z} \\ $$$$\: \\ $$$$\therefore{a}=\frac{{b}}{\mathrm{4}−{a}} \\ $$$$\because{a}\in\mathbb{Z},\:\:\:\frac{{b}}{\mathrm{4}−{a}}\in\mathbb{Z},\:\:\:\:\:\therefore\left(\mathrm{4}−{a}\right)\:\mathrm{is}\:\mathrm{a}\:\mathrm{factor} \\ $$